17:@0.922460:0.966765:0.939432:0.966765:0.939432:0.950778:0.922460:0.950778:0.000000:0.000000
En la práctica se presentan algunos productos de números reales a los :@0.108233:0.216661:0.599954:0.216661:0.599954:0.200164:0.108233:0.200164:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que se los desarrolla con la aplicación de las propiedades algebraicas :@0.108233:0.234012:0.599909:0.234012:0.599909:0.217514:0.108233:0.217514:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de los números reales. Así, cuando se escribe el lado derecho, como el :@0.108233:0.251363:0.599971:0.251363:0.599971:0.234865:0.108233:0.234865:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
producto del lado izquierdo, decimos que se ha factorado, y cuando :@0.108233:0.268714:0.599950:0.268714:0.599950:0.252216:0.108233:0.252216:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
realizamos el producto y obtenemos el lado derecho decimos que :@0.108233:0.286064:0.599975:0.286064:0.599975:0.269567:0.108233:0.269567:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
hemos aplicado la propiedad distributiva. A esos productos, de ma-:@0.108233:0.303415:0.595754:0.303415:0.595754:0.286917:0.108233:0.286917:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nera particular, se los conoce como productos notables.:@0.108233:0.320766:0.504957:0.320766:0.504957:0.304268:0.108233:0.304268:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Teorema. :@0.108233:0.349901:0.182192:0.349901:0.182192:0.332955:0.108233:0.332955:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para todo :@0.181903:0.349438:0.253819:0.349438:0.253819:0.332940:0.181903:0.332940:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a, b, x:@0.253530:0.349554:0.291155:0.349554:0.291155:0.333085:0.253530:0.333085:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.290962:0.349438:0.295104:0.349438:0.295104:0.332940:0.290962:0.332940:0.000000
 :@0.294803:0.348914:0.313677:0.348914:0.313677:0.335540:0.294803:0.335540:0.000000:0.000000
R:@0.313395:0.348463:0.327304:0.348463:0.327304:0.335017:0.313395:0.335017:0.000000
, se verifican las propiedades siguientes::@0.327111:0.349432:0.595777:0.349432:0.595777:0.332935:0.327111:0.332935:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i):@0.108239:0.367000:0.118777:0.367000:0.118777:0.350285:0.108239:0.350285:0.000000:0.000000
  (  +  ) (  +  ) =   + (  +  )   +  .:@0.118778:0.366783:0.382750:0.366783:0.382750:0.350285:0.118778:0.350285:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x a x b:@0.137928:0.366899:0.225353:0.366899:0.225353:0.350430:0.137928:0.350430:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.250398:0.366899:0.257873:0.366899:0.257873:0.350430:0.250398:0.350430:0.000000
2:@0.257872:0.360431:0.262825:0.360431:0.262825:0.350813:0.257872:0.350813:0.000000
a b x ab:@0.287869:0.366899:0.379995:0.366899:0.379995:0.350430:0.287869:0.350430:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ii) :@0.108240:0.384351:0.127120:0.384351:0.127120:0.367636:0.108240:0.367636:0.000000:0.000000:0.000000:0.000000
(  –  ) (  –  ) =   – (  +  )   +  .:@0.131975:0.384134:0.381827:0.384134:0.381827:0.367636:0.131975:0.367636:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x a x b:@0.137928:0.384249:0.224737:0.384249:0.224737:0.367781:0.137928:0.367781:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.249782:0.384249:0.257257:0.384249:0.257257:0.367781:0.249782:0.367781:0.000000
2:@0.257256:0.377782:0.262209:0.377782:0.262209:0.368164:0.257256:0.368164:0.000000
a b x ab:@0.286946:0.384249:0.379072:0.384249:0.379072:0.367781:0.286946:0.367781:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
iii):@0.108241:0.401701:0.127295:0.401701:0.127295:0.384987:0.108241:0.384987:0.000000:0.000000:0.000000:0.000000
  (  +  )  =   + 2  +  .:@0.127295:0.401484:0.300974:0.401484:0.300974:0.384987:0.127295:0.384987:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.137929:0.401600:0.175265:0.401600:0.175265:0.385131:0.137929:0.385131:0.000000:0.000000:0.000000
2:@0.181218:0.395133:0.186171:0.395133:0.186171:0.385515:0.181218:0.385515:0.000000
a:@0.205262:0.401600:0.214240:0.401600:0.214240:0.385131:0.205262:0.385131:0.000000
2:@0.214239:0.395133:0.219192:0.395133:0.219192:0.385515:0.214239:0.385515:0.000000
ab b:@0.246780:0.401600:0.293267:0.401600:0.293267:0.385131:0.246780:0.385131:0.000000:0.000000:0.000000:0.000000
2:@0.293267:0.395133:0.298220:0.395133:0.298220:0.385515:0.293267:0.385515:0.000000
iv) :@0.108225:0.419052:0.131112:0.419052:0.131112:0.402338:0.108225:0.402338:0.000000:0.000000:0.000000:0.000000
 (  –  )  =   – 2  +  .:@0.131112:0.418835:0.300357:0.418835:0.300357:0.402338:0.131112:0.402338:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.137912:0.418951:0.174940:0.418951:0.174940:0.402482:0.137912:0.402482:0.000000:0.000000:0.000000
2:@0.180910:0.412483:0.185863:0.412483:0.185863:0.402865:0.180910:0.402865:0.000000
a:@0.204954:0.418951:0.213931:0.418951:0.213931:0.402482:0.204954:0.402482:0.000000
2:@0.213931:0.412483:0.218884:0.412483:0.218884:0.402865:0.213931:0.402865:0.000000
ab b:@0.246164:0.418951:0.292651:0.418951:0.292651:0.402482:0.246164:0.402482:0.000000:0.000000:0.000000:0.000000
2:@0.292650:0.412483:0.297603:0.412483:0.297603:0.402865:0.292650:0.402865:0.000000
v):@0.108225:0.436403:0.122847:0.436403:0.122847:0.419688:0.108225:0.419688:0.000000:0.000000
  (  –  )  =   – 3:@0.122847:0.436186:0.246164:0.436186:0.246164:0.419688:0.122847:0.419688:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.137912:0.436302:0.174940:0.436302:0.174940:0.419833:0.137912:0.419833:0.000000:0.000000:0.000000
3:@0.180910:0.429834:0.185863:0.429834:0.185863:0.420216:0.180910:0.420216:0.000000
a:@0.204954:0.436302:0.213931:0.436302:0.213931:0.419833:0.204954:0.419833:0.000000
3:@0.213931:0.429834:0.218884:0.429834:0.218884:0.420216:0.213931:0.420216:0.000000
a b:@0.246164:0.436302:0.269360:0.436302:0.269360:0.419833:0.246164:0.419833:0.000000:0.000000:0.000000
2:@0.255142:0.429834:0.260095:0.429834:0.260095:0.420216:0.255142:0.420216:0.000000
 + 3:@0.269360:0.436186:0.296948:0.436186:0.296948:0.419688:0.269360:0.419688:0.000000:0.000000:0.000000:0.000000
ab:@0.296948:0.436302:0.315077:0.436302:0.315077:0.419833:0.296948:0.419833:0.000000:0.000000
2:@0.315077:0.429834:0.320030:0.429834:0.320030:0.420216:0.315077:0.420216:0.000000
 –  .:@0.320029:0.436186:0.355787:0.436186:0.355787:0.419688:0.320029:0.419688:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.338812:0.436302:0.348079:0.436302:0.348079:0.419833:0.338812:0.419833:0.000000
3:@0.348079:0.429834:0.353032:0.429834:0.353032:0.420216:0.348079:0.420216:0.000000
vi):@0.108229:0.453754:0.127090:0.453754:0.127090:0.437039:0.108229:0.437039:0.000000:0.000000:0.000000
  (  +  )  =   + 3:@0.127090:0.453537:0.246780:0.453537:0.246780:0.437039:0.127090:0.437039:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.137916:0.453652:0.175252:0.453652:0.175252:0.437184:0.137916:0.437184:0.000000:0.000000:0.000000
3:@0.181218:0.447185:0.186171:0.447185:0.186171:0.437567:0.181218:0.437567:0.000000
a:@0.205262:0.453652:0.214240:0.453652:0.214240:0.437184:0.205262:0.437184:0.000000
3:@0.214239:0.447185:0.219192:0.447185:0.219192:0.437567:0.214239:0.437567:0.000000
a b:@0.246780:0.453652:0.269977:0.453652:0.269977:0.437184:0.246780:0.437184:0.000000:0.000000:0.000000
2:@0.255758:0.447185:0.260711:0.447185:0.260711:0.437567:0.255758:0.437567:0.000000
 + 3:@0.269977:0.453537:0.297564:0.453537:0.297564:0.437039:0.269977:0.437039:0.000000:0.000000:0.000000:0.000000
ab:@0.297564:0.453652:0.315693:0.453652:0.315693:0.437184:0.297564:0.437184:0.000000:0.000000
2:@0.315693:0.447185:0.320646:0.447185:0.320646:0.437567:0.315693:0.437567:0.000000
 +  .:@0.320645:0.453537:0.356710:0.453537:0.356710:0.437039:0.320645:0.437039:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.339737:0.453652:0.349004:0.453652:0.349004:0.437184:0.339737:0.437184:0.000000
3:@0.349004:0.447185:0.353957:0.447185:0.353957:0.437567:0.349004:0.437567:0.000000
Demostración. :@0.108227:0.488701:0.225649:0.488701:0.225649:0.471755:0.108227:0.471755:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean :@0.225649:0.488238:0.263447:0.488238:0.263447:0.471741:0.225649:0.471741:0.000000:0.000000:0.000000:0.000000:0.000000
a, b, x:@0.263447:0.488354:0.301265:0.488354:0.301265:0.471885:0.263447:0.471885:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.301072:0.488238:0.305214:0.488238:0.305214:0.471741:0.301072:0.471741:0.000000
 :@0.305023:0.487720:0.323898:0.487720:0.323898:0.474346:0.305023:0.474346:0.000000:0.000000
R:@0.323722:0.487270:0.337632:0.487270:0.337632:0.473823:0.323722:0.473823:0.000000
, probaremos la propiedad :@0.337439:0.488238:0.528510:0.488238:0.528510:0.471741:0.337439:0.471741:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(  +  ) (  +  ) =   + (  +  )   +  . :@0.226606:0.505589:0.481532:0.505589:0.481532:0.489091:0.226606:0.489091:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x a x b:@0.232559:0.505705:0.319985:0.505705:0.319985:0.489236:0.232559:0.489236:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.345030:0.505705:0.352505:0.505705:0.352505:0.489236:0.345030:0.489236:0.000000
2:@0.352510:0.499237:0.357463:0.499237:0.357463:0.489619:0.352510:0.489619:0.000000
a b x ab:@0.382508:0.505705:0.474635:0.505705:0.474635:0.489236:0.382508:0.489236:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Por las propiedades distributiva, conmutativa de la adición y produc-:@0.108229:0.547419:0.595755:0.547419:0.595755:0.530921:0.108229:0.530921:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
to, se tiene::@0.108229:0.564770:0.187484:0.564770:0.187484:0.548272:0.108229:0.548272:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(  +  )(  +  ) =  (  +  )+ (  +  ) =   +   +   + :@0.108229:0.589249:0.449773:0.589249:0.449773:0.572751:0.108229:0.572751:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x a x b:@0.113835:0.589364:0.193304:0.589364:0.193304:0.572895:0.113835:0.572895:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x x b a x b:@0.216615:0.589364:0.328200:0.589364:0.328200:0.572895:0.216615:0.572895:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.351511:0.589364:0.358985:0.589364:0.358985:0.572895:0.351511:0.572895:0.000000
2:@0.358636:0.582896:0.363589:0.582896:0.363589:0.573277:0.358636:0.573277:0.000000
xb xa ab.:@0.381439:0.589364:0.469288:0.589364:0.469288:0.572895:0.381439:0.572895:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
                         = :@0.108238:0.606599:0.216721:0.606599:0.216721:0.590102:0.108238:0.590102:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x  + bx + ax + ab = x:@0.216335:0.606715:0.356704:0.606715:0.356704:0.590246:0.216335:0.590246:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.223418:0.600246:0.228371:0.600246:0.228371:0.590628:0.223418:0.590628:0.000000
2:@0.356314:0.600246:0.361267:0.600246:0.361267:0.590628:0.356314:0.590628:0.000000
 + (:@0.361043:0.606599:0.384932:0.606599:0.384932:0.590102:0.361043:0.590102:0.000000:0.000000:0.000000:0.000000
a + b x + ab.:@0.384547:0.606715:0.470489:0.606715:0.470489:0.590246:0.384547:0.590246:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
):@0.420034:0.606599:0.425987:0.606599:0.425987:0.590102:0.420034:0.590102:0.000000
Nótese que :@0.108245:0.641301:0.194493:0.641301:0.194493:0.624803:0.108245:0.624803:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ax + bx =  a + b x.:@0.194493:0.641417:0.325805:0.641417:0.325805:0.624948:0.194493:0.624948:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.266045:0.641301:0.271998:0.641301:0.271998:0.624803:0.266045:0.624803:0.000000
):@0.309411:0.641301:0.315364:0.641301:0.315364:0.624803:0.309411:0.624803:0.000000
Conclusión::@0.108245:0.676465:0.198753:0.676465:0.198753:0.659519:0.108245:0.659519:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.198753:0.676465:0.202779:0.676465:0.202779:0.659519:0.198753:0.659519:0.000000
(:@0.202779:0.676002:0.208732:0.676002:0.208732:0.659505:0.202779:0.659505:0.000000
x + a x + b = x:@0.208732:0.676118:0.324767:0.676118:0.324767:0.659649:0.208732:0.659649:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
)(:@0.244354:0.676002:0.256260:0.676002:0.256260:0.659505:0.244354:0.659505:0.000000:0.000000
) :@0.292170:0.676002:0.302265:0.676002:0.302265:0.659505:0.292170:0.659505:0.000000:0.000000
2:@0.324751:0.669649:0.329704:0.669649:0.329704:0.660031:0.324751:0.660031:0.000000
 + (:@0.329703:0.676002:0.354748:0.676002:0.354748:0.659505:0.329703:0.659505:0.000000:0.000000:0.000000:0.000000
a + b x + ab.:@0.354748:0.676118:0.445314:0.676118:0.445314:0.659649:0.354748:0.659649:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
):@0.392161:0.676002:0.398114:0.676002:0.398114:0.659505:0.392161:0.659505:0.000000
Teorema. :@0.108230:0.705137:0.182189:0.705137:0.182189:0.688191:0.108230:0.688191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para todo :@0.181996:0.704674:0.254010:0.704674:0.254010:0.688177:0.181996:0.688177:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a, b :@0.253817:0.704790:0.282118:0.704790:0.282118:0.688321:0.253817:0.688321:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.281925:0.704150:0.300799:0.704150:0.300799:0.690777:0.281925:0.690777:0.000000:0.000000
R:@0.300624:0.703700:0.314534:0.703700:0.314534:0.690253:0.300624:0.690253:0.000000
, se verifican las propiedades siguientes::@0.314341:0.704669:0.583486:0.704669:0.583486:0.688171:0.314341:0.688171:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i):@0.108241:0.722236:0.118780:0.722236:0.118780:0.705522:0.108241:0.705522:0.000000:0.000000
  (:@0.118779:0.722020:0.137929:0.722020:0.137929:0.705522:0.118779:0.705522:0.000000:0.000000:0.000000
a – b a + b:@0.137929:0.722135:0.227956:0.722135:0.227956:0.705666:0.137929:0.705666:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
) (:@0.174495:0.722020:0.190543:0.722020:0.190543:0.705522:0.174495:0.705522:0.000000:0.000000:0.000000
) =   –  .:@0.227956:0.722020:0.302687:0.722020:0.302687:0.705522:0.227956:0.705522:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.253001:0.722135:0.261978:0.722135:0.261978:0.705666:0.253001:0.705666:0.000000
2:@0.261976:0.715667:0.266930:0.715667:0.266930:0.706048:0.261976:0.706048:0.000000
b:@0.285712:0.722135:0.294979:0.722135:0.294979:0.705666:0.285712:0.705666:0.000000
2:@0.294979:0.715667:0.299932:0.715667:0.299932:0.706048:0.294979:0.706048:0.000000
ii) :@0.108243:0.739587:0.127123:0.739587:0.127123:0.722873:0.108243:0.722873:0.000000:0.000000:0.000000:0.000000
a:@0.131978:0.739486:0.140956:0.739486:0.140956:0.723017:0.131978:0.723017:0.000000
3:@0.140954:0.733017:0.145907:0.733017:0.145907:0.723399:0.140954:0.723399:0.000000
 –  = (:@0.145908:0.739370:0.203955:0.739370:0.203955:0.722873:0.145908:0.722873:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 b:@0.160549:0.739486:0.173958:0.739486:0.173958:0.723017:0.160549:0.723017:0.000000:0.000000
3:@0.173958:0.733017:0.178911:0.733017:0.178911:0.723399:0.173958:0.723399:0.000000
a – b a:@0.203955:0.739486:0.261404:0.739486:0.261404:0.723017:0.203955:0.723017:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
)(  + :@0.240520:0.739370:0.285447:0.739370:0.285447:0.722873:0.240520:0.722873:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.261402:0.733017:0.266355:0.733017:0.266355:0.723399:0.261402:0.723399:0.000000
ab + b:@0.285447:0.739486:0.332012:0.739486:0.332012:0.723017:0.285447:0.723017:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.332010:0.733017:0.336963:0.733017:0.336963:0.723399:0.332010:0.723399:0.000000
).:@0.336962:0.739370:0.345670:0.739370:0.345670:0.722873:0.336962:0.722873:0.000000:0.000000
iii) :@0.108226:0.756938:0.131363:0.756938:0.131363:0.740223:0.108226:0.740223:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.131961:0.756837:0.140939:0.756837:0.140939:0.740368:0.131961:0.740368:0.000000
3:@0.140954:0.750368:0.145907:0.750368:0.145907:0.740750:0.140954:0.740750:0.000000
 +   = (:@0.145908:0.756721:0.204263:0.756721:0.204263:0.740223:0.145908:0.740223:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.164999:0.756837:0.174266:0.756837:0.174266:0.740368:0.164999:0.740368:0.000000
3:@0.174264:0.750368:0.179217:0.750368:0.179217:0.740750:0.174264:0.740750:0.000000
a + b a:@0.204263:0.756837:0.262559:0.756837:0.262559:0.740368:0.204263:0.740368:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
)(  –   +  ).:@0.241676:0.756721:0.346440:0.756721:0.346440:0.740223:0.241676:0.740223:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.262558:0.750368:0.267511:0.750368:0.267511:0.740750:0.262558:0.740750:0.000000
ab b:@0.286293:0.756837:0.332781:0.756837:0.332781:0.740368:0.286293:0.740368:0.000000:0.000000:0.000000:0.000000
2:@0.332781:0.750368:0.337734:0.750368:0.337734:0.740750:0.332781:0.740750:0.000000
iv) :@0.108226:0.774289:0.131113:0.774289:0.131113:0.757574:0.108226:0.757574:0.000000:0.000000:0.000000:0.000000
a:@0.131961:0.774187:0.140939:0.774187:0.140939:0.757719:0.131961:0.757719:0.000000
4:@0.140954:0.767719:0.145907:0.767719:0.145907:0.758101:0.140954:0.758101:0.000000
 –   = (:@0.145908:0.774072:0.203955:0.774072:0.203955:0.757574:0.145908:0.757574:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.164691:0.774187:0.173958:0.774187:0.173958:0.757719:0.164691:0.757719:0.000000
4:@0.173958:0.767719:0.178911:0.767719:0.178911:0.758101:0.173958:0.758101:0.000000
a – b a  b:@0.203955:0.774187:0.293904:0.774187:0.293904:0.757719:0.203955:0.757719:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
) (  + )(a  :@0.240520:0.774072:0.322743:0.774072:0.322743:0.757574:0.240520:0.757574:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.313648:0.767719:0.318601:0.767719:0.318601:0.758101:0.313648:0.758101:0.000000
+ b:@0.322743:0.774187:0.347037:0.774187:0.347037:0.757719:0.322743:0.757719:0.000000:0.000000:0.000000
2:@0.347037:0.767719:0.351990:0.767719:0.351990:0.758101:0.347037:0.758101:0.000000
) = (  –  ) (  + ). :@0.351989:0.774072:0.506058:0.774072:0.506058:0.757574:0.351989:0.757574:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.382987:0.774187:0.391964:0.774187:0.391964:0.757719:0.382987:0.757719:0.000000
2:@0.391963:0.767719:0.396917:0.767719:0.396917:0.758101:0.391963:0.758101:0.000000
b:@0.415701:0.774187:0.424967:0.774187:0.424967:0.757719:0.415701:0.757719:0.000000
2:@0.424967:0.767719:0.429920:0.767719:0.429920:0.758101:0.424967:0.758101:0.000000
a:@0.445967:0.774187:0.454945:0.774187:0.454945:0.757719:0.445967:0.757719:0.000000
2:@0.454944:0.767719:0.459897:0.767719:0.459897:0.758101:0.454944:0.758101:0.000000
 b:@0.474848:0.774187:0.488256:0.774187:0.488256:0.757719:0.474848:0.757719:0.000000:0.000000
2:@0.488256:0.767719:0.493209:0.767719:0.493209:0.758101:0.488256:0.758101:0.000000
v) :@0.108231:0.791639:0.126937:0.791639:0.126937:0.774925:0.108231:0.774925:0.000000:0.000000:0.000000
a:@0.131966:0.791538:0.140944:0.791538:0.140944:0.775069:0.131966:0.775069:0.000000
4:@0.140954:0.785070:0.145907:0.785070:0.145907:0.775451:0.140954:0.775451:0.000000
 + :@0.145908:0.791423:0.164999:0.791423:0.164999:0.774925:0.145908:0.774925:0.000000:0.000000:0.000000
a b:@0.164999:0.791538:0.188196:0.791538:0.188196:0.775069:0.164999:0.775069:0.000000:0.000000:0.000000
2 2:@0.173976:0.785070:0.193149:0.785070:0.193149:0.775451:0.173976:0.775451:0.000000:0.000000:0.000000
 +   = (  – :@0.193149:0.791423:0.284218:0.791423:0.284218:0.774925:0.193149:0.774925:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.212241:0.791538:0.221508:0.791538:0.221508:0.775069:0.212241:0.775069:0.000000
4:@0.221506:0.785070:0.226459:0.785070:0.226459:0.775451:0.221506:0.775451:0.000000
a:@0.251505:0.791538:0.260482:0.791538:0.260482:0.775069:0.251505:0.775069:0.000000
2:@0.260481:0.785070:0.265434:0.785070:0.265434:0.775451:0.260481:0.775451:0.000000
ab + b a:@0.284218:0.791538:0.356617:0.791538:0.356617:0.775069:0.284218:0.775069:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.330780:0.785070:0.335733:0.785070:0.335733:0.775451:0.330780:0.775451:0.000000
)(  +   +  ).:@0.335734:0.791423:0.440808:0.791423:0.440808:0.774925:0.335734:0.774925:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.356617:0.785070:0.361571:0.785070:0.361571:0.775451:0.356617:0.775451:0.000000
ab b:@0.380661:0.791538:0.427148:0.791538:0.427148:0.775069:0.380661:0.775069:0.000000:0.000000:0.000000:0.000000
2:@0.427147:0.785070:0.432100:0.785070:0.432100:0.775451:0.427147:0.775451:0.000000
Demostración.:@0.108232:0.826587:0.221628:0.826587:0.221628:0.809641:0.108232:0.809641:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Sean :@0.221628:0.826124:0.263568:0.826124:0.263568:0.809626:0.221628:0.809626:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a, b :@0.263568:0.826240:0.291869:0.826240:0.291869:0.809771:0.263568:0.809771:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.291673:0.825605:0.310548:0.825605:0.310548:0.812232:0.291673:0.812232:0.000000:0.000000
R:@0.310372:0.825155:0.324282:0.825155:0.324282:0.811708:0.310372:0.811708:0.000000
, probaremos la propiedad :@0.324089:0.826124:0.515160:0.826124:0.515160:0.809626:0.324089:0.809626:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
iv.:@0.515160:0.826240:0.528282:0.826240:0.528282:0.809771:0.515160:0.809771:0.000000:0.000000:0.000000
En primer lugar, por la parte   tenemos (:@0.108241:0.860826:0.414251:0.860826:0.414251:0.844328:0.108241:0.844328:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i,:@0.325900:0.860941:0.332585:0.860941:0.332585:0.844472:0.325900:0.844472:0.000000:0.000000
a – b a + b:@0.414231:0.860941:0.510596:0.860941:0.510596:0.844472:0.414231:0.844472:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
)(:@0.456037:0.860826:0.467943:0.860826:0.467943:0.844328:0.456037:0.844328:0.000000:0.000000
) =   –  . :@0.510596:0.860826:0.599909:0.860826:0.599909:0.844328:0.510596:0.844328:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.540881:0.860941:0.549859:0.860941:0.549859:0.844472:0.540881:0.844472:0.000000
2:@0.549828:0.854473:0.554781:0.854473:0.554781:0.844854:0.549828:0.844854:0.000000
b:@0.578804:0.860941:0.588070:0.860941:0.588070:0.844472:0.578804:0.844472:0.000000
2:@0.588060:0.854473:0.593013:0.854473:0.593013:0.844854:0.588060:0.844854:0.000000
 :@0.595767:0.860826:0.599909:0.860826:0.599909:0.844328:0.595767:0.844328:0.000000
Luego, por la misma propiedad, se tiene que (  –  )(  +  ) =   –  , :@0.108241:0.895527:0.599909:0.895527:0.599909:0.879029:0.108241:0.879029:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.423170:0.895643:0.432147:0.895643:0.432147:0.879174:0.423170:0.879174:0.000000
2:@0.432117:0.889174:0.437070:0.889174:0.437070:0.879556:0.432117:0.879556:0.000000
b a:@0.453812:0.895643:0.488911:0.895643:0.488911:0.879174:0.453812:0.879174:0.000000:0.000000:0.000000
2:@0.463074:0.889174:0.468027:0.889174:0.468027:0.879556:0.463074:0.879556:0.000000
2:@0.488909:0.889174:0.493863:0.889174:0.493863:0.879556:0.488909:0.879556:0.000000
b:@0.510913:0.895643:0.520180:0.895643:0.520180:0.879174:0.510913:0.879174:0.000000
2:@0.520174:0.889174:0.525128:0.889174:0.525128:0.879556:0.520174:0.879556:0.000000
a:@0.548131:0.895643:0.557109:0.895643:0.557109:0.879174:0.548131:0.879174:0.000000
4:@0.557103:0.889174:0.562057:0.889174:0.562057:0.879556:0.557103:0.879556:0.000000
b:@0.578797:0.895643:0.588064:0.895643:0.588064:0.879174:0.578797:0.879174:0.000000
4:@0.588060:0.889174:0.593013:0.889174:0.593013:0.879556:0.588060:0.879556:0.000000
 :@0.595767:0.895527:0.599909:0.895527:0.599909:0.879029:0.595767:0.879029:0.000000
o también que (:@0.108241:0.912878:0.223175:0.912878:0.223175:0.896380:0.108241:0.896380:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a – b a + b a:@0.223175:0.912994:0.329943:0.912994:0.329943:0.896525:0.223175:0.896525:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
)(:@0.259741:0.912878:0.271647:0.912878:0.271647:0.896380:0.259741:0.896380:0.000000:0.000000
)(  +  ) =   –  .:@0.309060:0.912878:0.442930:0.912878:0.442930:0.896380:0.309060:0.896380:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.329934:0.906525:0.334887:0.906525:0.334887:0.896907:0.329934:0.896907:0.000000
b:@0.353978:0.912994:0.363245:0.912994:0.363245:0.896525:0.353978:0.896525:0.000000
2:@0.363245:0.906525:0.368198:0.906525:0.368198:0.896907:0.363245:0.896907:0.000000
a:@0.393242:0.912994:0.402219:0.912994:0.402219:0.896525:0.393242:0.896525:0.000000
4:@0.402219:0.906525:0.407172:0.906525:0.407172:0.896907:0.402219:0.896907:0.000000
b:@0.425956:0.912994:0.435223:0.912994:0.435223:0.896525:0.425956:0.896525:0.000000
4:@0.435221:0.906525:0.440175:0.906525:0.440175:0.896907:0.435221:0.896907:0.000000
El resto de propiedades se propone como ejercicio.:@0.108235:0.930229:0.469645:0.930229:0.469645:0.913731:0.108235:0.913731:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Utilicen esos volúmenes para comprobar que::@0.108235:0.104983:0.433696:0.104983:0.433696:0.088486:0.108235:0.088486:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(  +  )  =   + 3:@0.108235:0.122334:0.223036:0.122337:0.223036:0.105840:0.108235:0.105836:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.114188:0.122450:0.151524:0.122450:0.151524:0.105981:0.114188:0.105981:0.000000:0.000000:0.000000
3:@0.157472:0.115986:0.162425:0.115986:0.162425:0.106367:0.157472:0.106367:0.000000
a:@0.181517:0.122453:0.190495:0.122453:0.190495:0.105984:0.181517:0.105984:0.000000
3:@0.190494:0.115986:0.195447:0.115986:0.195447:0.106367:0.190494:0.106367:0.000000
a b:@0.223036:0.122453:0.246232:0.122453:0.246232:0.105984:0.223036:0.105984:0.000000:0.000000:0.000000
2:@0.232011:0.115986:0.236965:0.115986:0.236965:0.106367:0.232011:0.106367:0.000000
 + 3:@0.246232:0.122337:0.273820:0.122337:0.273820:0.105840:0.246232:0.105840:0.000000:0.000000:0.000000:0.000000
ab:@0.273820:0.122453:0.291948:0.122453:0.291948:0.105984:0.273820:0.105984:0.000000:0.000000
2:@0.291947:0.115986:0.296900:0.115986:0.296900:0.106367:0.291947:0.106367:0.000000
 +  .:@0.296900:0.122337:0.332966:0.122337:0.332966:0.105840:0.296900:0.105840:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.315992:0.122453:0.325259:0.122453:0.325259:0.105984:0.315992:0.105984:0.000000
3:@0.325257:0.115986:0.330210:0.115986:0.330210:0.106367:0.325257:0.106367:0.000000
Con los siguientes valores,   = 1,4 cm;   = 2,6 cm, calculen los volú-:@0.108236:0.157039:0.595697:0.157039:0.595697:0.140541:0.108236:0.140541:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.299787:0.157154:0.308765:0.157154:0.308765:0.140686:0.299787:0.140686:0.000000
b:@0.385151:0.157154:0.394418:0.157154:0.394418:0.140686:0.385151:0.140686:0.000000
menes de cada uno de los paralelepípedos rectangulares y verifiquen :@0.108236:0.174390:0.599899:0.174390:0.599899:0.157892:0.108236:0.157892:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que su suma sea 64 cm .:@0.108236:0.191740:0.279961:0.191740:0.279961:0.175243:0.108236:0.175243:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.272252:0.185389:0.277206:0.185389:0.277206:0.175770:0.272252:0.175770:0.000000
Glosario:@0.684804:0.565780:0.752269:0.565780:0.752269:0.548098:0.684804:0.548098:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
algoritmo.:@0.685042:0.592594:0.754118:0.592594:0.754118:0.577332:0.685042:0.577332:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Conjunto or-:@0.754118:0.592396:0.842613:0.592396:0.842613:0.577332:0.754118:0.577332:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
denado y finito de operaciones :@0.638498:0.608238:0.844036:0.608238:0.844036:0.593174:0.638498:0.593174:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que permite hallar la solución :@0.638498:0.624080:0.834310:0.624080:0.834310:0.609016:0.638498:0.609016:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de un problema.:@0.638498:0.639922:0.745653:0.639922:0.745653:0.624858:0.638498:0.624858:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
torsión. :@0.638498:0.663090:0.693467:0.663090:0.693467:0.647829:0.638498:0.647829:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Acción y efecto de :@0.693467:0.662892:0.818757:0.662892:0.818757:0.647829:0.693467:0.647829:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
torcer o torcerse algo en forma :@0.638498:0.678734:0.842138:0.678734:0.842138:0.663671:0.638498:0.663671:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
helicoidal.:@0.638498:0.694576:0.702929:0.694576:0.702929:0.679513:0.638498:0.679513:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.632070:0.569512:0.643474:0.568003:0.638272:0.545858:0.626867:0.547367:0.000000
c:@0.635451:0.580481:0.646050:0.579079:0.640968:0.557444:0.630369:0.558847:0.000000
b:@0.645827:0.573264:0.658540:0.571581:0.653408:0.549739:0.640695:0.551421:0.000000
Shutterstock, 105363371:@0.870772:0.390982:0.870772:0.322808:0.859303:0.322808:0.859303:0.390982:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.685591:0.101352:0.783214:0.101352:0.783214:0.085879:0.685591:0.085879:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.685591:0.113920:0.769654:0.113920:0.769654:0.098447:0.685591:0.098447:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los productos notables :@0.685829:0.138394:0.842289:0.138394:0.842289:0.123331:0.685829:0.123331:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
son muy utilizados en ingenie-:@0.639286:0.154236:0.836662:0.154236:0.836662:0.139173:0.639286:0.139173:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ría. Por ejemplo, para calcular la :@0.639286:0.170078:0.846529:0.170078:0.846529:0.155015:0.639286:0.155015:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
intensidad en circuitos eléctri-:@0.639286:0.185920:0.833603:0.185920:0.833603:0.170857:0.639286:0.170857:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cos, para calcular la :@0.639286:0.201762:0.767499:0.201762:0.767499:0.186699:0.639286:0.186699:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
torsión:@0.767499:0.201960:0.815712:0.201960:0.815712:0.186699:0.767499:0.186699:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 en :@0.815714:0.201762:0.839302:0.201762:0.839302:0.186699:0.815714:0.186699:0.000000:0.000000:0.000000:0.000000
estructuras o para calcular el :@0.639286:0.217604:0.827742:0.217604:0.827742:0.202541:0.639286:0.202541:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
número de individuos en un :@0.639286:0.233446:0.827532:0.233446:0.827532:0.218383:0.639286:0.218383:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
algoritmo:@0.639286:0.249486:0.705354:0.249486:0.705354:0.234225:0.639286:0.234225:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 genético.:@0.705354:0.249288:0.766954:0.249288:0.766954:0.234225:0.705354:0.234225:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.639292:0.409557:0.650773:0.409557:0.650773:0.399533:0.639292:0.399533:0.000000
 :@0.650773:0.410265:0.653654:0.410265:0.653654:0.398788:0.650773:0.398788:0.000000
Medición de una placa de circuito  :@0.653654:0.410265:0.828573:0.410265:0.828573:0.398788:0.653654:0.398788:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
eléctrico:@0.639287:0.422335:0.681582:0.422335:0.681582:0.410858:0.639287:0.410858:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Indaga escribe :@0.639292:0.447997:0.755102:0.447997:0.755102:0.432525:0.639292:0.432525:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 y :@0.686925:0.447575:0.701630:0.447575:0.701630:0.432512:0.686925:0.432512:0.000000:0.000000:0.000000
en el cuader-:@0.755102:0.447575:0.838112:0.447575:0.838112:0.432512:0.755102:0.432512:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
no otras de las aplicaciones de :@0.639292:0.463417:0.839991:0.463417:0.839991:0.448354:0.639292:0.448354:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los productos notables.:@0.639292:0.479259:0.791038:0.479259:0.791038:0.464196:0.639292:0.464196:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.684804:0.757566:0.782426:0.757566:0.782426:0.742094:0.684804:0.742094:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
socioemocional:@0.684804:0.770134:0.795179:0.770134:0.795179:0.754662:0.684804:0.754662:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Hay ocasiones en que :@0.685042:0.794607:0.829735:0.794607:0.829735:0.779544:0.685042:0.779544:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
consideramos que la matemá-:@0.638498:0.810449:0.834273:0.810449:0.834273:0.795386:0.638498:0.795386:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tica no tiene aplicación o que :@0.638498:0.826291:0.833957:0.826291:0.833957:0.811228:0.638498:0.811228:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es muy difícil. :@0.638498:0.842133:0.729261:0.842133:0.729261:0.827070:0.638498:0.827070:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Reflexiona:@0.729261:0.842556:0.802346:0.842556:0.802346:0.827083:0.729261:0.827083:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 sobre :@0.802349:0.842133:0.845638:0.842133:0.845638:0.827070:0.802349:0.827070:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
las siguientes interrogantes y :@0.638498:0.857975:0.826376:0.857975:0.826376:0.842912:0.638498:0.842912:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
comenta:@0.638498:0.874240:0.700574:0.874240:0.700574:0.858767:0.638498:0.858767:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 en la clase: ¿te has :@0.700574:0.873817:0.823440:0.873817:0.823440:0.858754:0.700574:0.858754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
puesto a pensar que pasaría :@0.638498:0.889659:0.822314:0.889659:0.822314:0.874596:0.638498:0.874596:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
si no existieran los números?, :@0.638498:0.905501:0.828521:0.905501:0.828521:0.890438:0.638498:0.890438:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿como sería la sociedad?:@0.638498:0.921343:0.796013:0.921343:0.796013:0.906280:0.638498:0.906280:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 ©:@0.079553:0.731952:0.079553:0.720342:0.061505:0.720342:0.061505:0.731952:0.000000:0.000000
maya:@0.080774:0.720340:0.080774:0.684191:0.055786:0.684191:0.055786:0.720340:0.000000:0.000000:0.000000:0.000000
®EDUCACIÓN – Libro resuelto solo para fines didácticos – Prohibida su reproducción :@0.079553:0.684191:0.079553:0.268044:0.061505:0.268044:0.061505:0.684191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000