112:@0.052592:0.966074:0.080768:0.966074:0.080768:0.949450:0.052592:0.949450:0.000000:0.000000:0.000000 Tema 5:@0.124729:0.083964:0.219414:0.083964:0.219414:0.055923:0.124729:0.055923:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Triángulo de Pascal y teorema del binomio:@0.305293:0.083059:0.856779:0.083059:0.856779:0.055403:0.305293:0.055403:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Blaise Pascal, con su análisis del triángulo que lleva su apellido, contribuyó a la :@0.304744:0.243344:0.907047:0.243344:0.907047:0.227675:0.304744:0.227675:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 conformación de teorías matemáticas, como también lo hicieron los trabajos del :@0.304744:0.259941:0.907141:0.259941:0.907141:0.244271:0.304744:0.244271:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ecuatoriano de origen alemán, Peter Thullen.:@0.304744:0.276537:0.632734:0.276537:0.632734:0.260867:0.304744:0.260867:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ¿Qué estructura tiene el triángulo denominado triángulo de Pascal que se observa :@0.304744:0.300256:0.907174:0.300256:0.907174:0.284586:0.304744:0.284586:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 en la imagen?:@0.304744:0.316852:0.407072:0.316852:0.407072:0.301183:0.304744:0.301183:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Se trata de un triángulo simétrico de números enteros. Está conformado por filas :@0.304744:0.340571:0.907045:0.340571:0.907045:0.324902:0.304744:0.324902:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 que tienen 1 al inicio y al final de cada fila. Empieza con un 1 en la primera fila, y en :@0.304744:0.357168:0.907123:0.357168:0.907123:0.341498:0.304744:0.341498:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 las filas siguientes muestra números de forma que cada uno de ellos son la suma :@0.304744:0.373764:0.907180:0.373764:0.907180:0.358094:0.304744:0.358094:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de los dos números que tiene encima. :@0.304744:0.390361:0.588398:0.390361:0.588398:0.374691:0.304744:0.374691:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.304744:0.603887:0.308779:0.603887:0.308779:0.588217:0.304744:0.588217:0.000000 Ejemplo 1:@0.304744:0.648008:0.374249:0.648008:0.374249:0.632895:0.304744:0.632895:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Obtener la fila 9 y 10 del triángulo de Pascal.:@0.304744:0.672046:0.627056:0.672046:0.627056:0.656376:0.304744:0.656376:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Solución:@0.304744:0.693948:0.365404:0.693948:0.365404:0.678836:0.304744:0.678836:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Para obtener la fila 9, sumamos los números de la fila 8.:@0.304744:0.717987:0.707106:0.717987:0.707106:0.702317:0.304744:0.702317:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.304744:0.741706:0.308779:0.741706:0.308779:0.726036:0.304744:0.726036:0.000000 Para formar la fila 10, sumamos los obtenidos de la fila 9.:@0.304744:0.816403:0.715490:0.816403:0.715490:0.800734:0.304744:0.800734:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 En el triángulo de Pascal :@0.105654:0.678091:0.270414:0.678091:0.270414:0.663846:0.105654:0.663846:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 se observan algunas :@0.105654:0.693179:0.245166:0.693179:0.245166:0.678934:0.105654:0.678934:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 particularidades. Por :@0.105654:0.708267:0.244748:0.708267:0.244748:0.694021:0.105654:0.694021:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ejemplo, al sumar los :@0.105654:0.723354:0.249489:0.723354:0.249489:0.709109:0.105654:0.709109:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 números de la fila, se :@0.105654:0.738442:0.248586:0.738442:0.248586:0.724197:0.105654:0.724197:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 obtienen las potencias :@0.105654:0.753529:0.260277:0.753529:0.260277:0.739284:0.105654:0.739284:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de 2.:@0.105654:0.768617:0.137651:0.768617:0.137651:0.754372:0.105654:0.754372:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.105654:0.790834:0.109323:0.790834:0.109323:0.776588:0.105654:0.776588:0.000000 Recuerda que...:@0.135707:0.653065:0.257788:0.653065:0.257788:0.636164:0.135707:0.636164:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Desarrolla:@0.311168:0.166194:0.392489:0.166194:0.392489:0.149293:0.311168:0.149293:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 los binomios::@0.392489:0.166194:0.493676:0.166194:0.493676:0.150524:0.392489:0.150524:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Saberes previos:@0.344861:0.139565:0.470369:0.139565:0.470369:0.122665:0.344861:0.122665:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.164012:0.790361:0.168999:0.790361:0.168999:0.781545:0.164012:0.781545:0.000000 1:@0.246915:0.790361:0.251902:0.790361:0.251902:0.781545:0.246915:0.781545:0.000000 2:@0.246098:0.801444:0.251086:0.801444:0.251086:0.792628:0.246098:0.792628:0.000000 4:@0.246098:0.812557:0.251086:0.812557:0.251086:0.803740:0.246098:0.803740:0.000000 8:@0.246098:0.823544:0.251086:0.823544:0.251086:0.814728:0.246098:0.814728:0.000000 16:@0.243600:0.834488:0.253575:0.834488:0.253575:0.825671:0.243600:0.825671:0.000000:0.000000 32:@0.243600:0.845365:0.253575:0.845365:0.253575:0.836549:0.243600:0.836549:0.000000:0.000000 64:@0.243600:0.856272:0.253575:0.856272:0.253575:0.847456:0.243600:0.847456:0.000000:0.000000 128:@0.244630:0.867077:0.259593:0.867077:0.259593:0.858260:0.244630:0.858260:0.000000:0.000000:0.000000 1:@0.171187:0.801444:0.176175:0.801444:0.176175:0.792628:0.171187:0.792628:0.000000 1:@0.178372:0.812557:0.183360:0.812557:0.183360:0.803740:0.178372:0.803740:0.000000 1:@0.185557:0.823544:0.190544:0.823544:0.190544:0.814728:0.185557:0.814728:0.000000 1:@0.192742:0.834488:0.197729:0.834488:0.197729:0.825671:0.192742:0.825671:0.000000 1:@0.199926:0.845365:0.204914:0.845365:0.204914:0.836549:0.199926:0.836549:0.000000 1:@0.207111:0.856272:0.212099:0.856272:0.212099:0.847456:0.207111:0.847456:0.000000 1:@0.214296:0.867077:0.219284:0.867077:0.219284:0.858260:0.214296:0.858260:0.000000 1 7 21 35 35 21 7:@0.113689:0.867077:0.204904:0.867077:0.204904:0.858260:0.113689:0.858260:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1 6 15:@0.120873:0.856272:0.157089:0.856272:0.157089:0.847456:0.120873:0.847456:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1 5 10:@0.128282:0.845365:0.164284:0.845365:0.164284:0.836549:0.128282:0.836549:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1 4:@0.135243:0.834488:0.154601:0.834488:0.154601:0.825671:0.135243:0.825671:0.000000:0.000000:0.000000 1 3 3:@0.142428:0.823544:0.176155:0.823544:0.176155:0.814728:0.142428:0.814728:0.000000:0.000000:0.000000:0.000000:0.000000 1 2:@0.149613:0.812557:0.168970:0.812557:0.168970:0.803740:0.149613:0.803740:0.000000:0.000000:0.000000 1:@0.156798:0.801444:0.161785:0.801444:0.161785:0.792628:0.156798:0.792628:0.000000 4:@0.178352:0.834488:0.183340:0.834488:0.183340:0.825671:0.178352:0.825671:0.000000 6:@0.163983:0.834488:0.168970:0.834488:0.168970:0.825671:0.163983:0.825671:0.000000 6:@0.192732:0.856272:0.197719:0.856272:0.197719:0.847456:0.192732:0.847456:0.000000 5:@0.185547:0.845365:0.190535:0.845365:0.190535:0.836549:0.185547:0.836549:0.000000 10:@0.168679:0.845365:0.178654:0.845365:0.178654:0.836549:0.168679:0.836549:0.000000:0.000000 20 15:@0.161494:0.856272:0.185839:0.856272:0.185839:0.847456:0.161494:0.847456:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.413899:0.197752:0.420035:0.197752:0.420035:0.177351:0.413899:0.177351:0.000000 ):@0.464372:0.197752:0.470509:0.197752:0.470509:0.177351:0.464372:0.177351:0.000000 −:@0.442378:0.195880:0.452495:0.195880:0.452495:0.180307:0.442378:0.180307:0.000000 =:@0.480431:0.195880:0.490548:0.195880:0.490548:0.180307:0.480431:0.180307:0.000000 x:@0.431018:0.195202:0.438481:0.195202:0.438481:0.178841:0.431018:0.178841:0.000000 2:@0.420754:0.195202:0.429747:0.195202:0.429747:0.179533:0.420754:0.179533:0.000000 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:@0.517725:0.580684:0.697479:0.580684:0.697479:0.565107:0.517725:0.565107:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 21:@0.696976:0.580684:0.715404:0.580684:0.715404:0.565107:0.696976:0.565107:0.000000:0.000000 :@0.715236:0.580684:0.817074:0.580684:0.817074:0.565107:0.715236:0.565107:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 7:@0.761339:0.580684:0.770636:0.580684:0.770636:0.565107:0.761339:0.565107:0.000000 1:@0.816571:0.580684:0.825869:0.580684:0.825869:0.565107:0.816571:0.565107:0.000000 1:@0.600951:0.415576:0.610249:0.415576:0.610249:0.399998:0.600951:0.399998:0.000000 1:@0.183609:0.298539:0.191784:0.298539:0.191784:0.284293:0.183609:0.284293:0.000000 1 1:@0.170693:0.309226:0.203058:0.309226:0.203058:0.294980:0.170693:0.294980:0.000000:0.000000:0.000000 1:@0.157777:0.319410:0.165952:0.319410:0.165952:0.305165:0.157777:0.305165:0.000000 1 3 3:@0.147424:0.331015:0.203025:0.331015:0.203025:0.316769:0.147424:0.316769:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.134508:0.341702:0.142683:0.341702:0.142683:0.327456:0.134508:0.327456:0.000000 1:@0.117738:0.353294:0.125914:0.353294:0.125914:0.339049:0.117738:0.339049:0.000000 1 6 15 20:@0.103499:0.365238:0.195955:0.365238:0.195955:0.350993:0.103499:0.350993:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.264238:0.365238:0.272413:0.365238:0.272413:0.350993:0.264238:0.350993:0.000000 8 28 56 70:@0.094938:0.389454:0.198016:0.389454:0.198016:0.375209:0.094938:0.375209:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 7 21 35 35:@0.111674:0.377183:0.214751:0.377183:0.214751:0.362938:0.111674:0.362938:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5 10 10:@0.143721:0.353294:0.211200:0.353294:0.211200:0.339049:0.143721:0.339049:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 4 6:@0.161228:0.341702:0.192337:0.341702:0.192337:0.327456:0.161228:0.327456:0.000000:0.000000:0.000000 2 1:@0.183609:0.319410:0.214299:0.319410:0.214299:0.305165:0.183609:0.305165:0.000000:0.000000:0.000000 4:@0.206091:0.341702:0.214266:0.341702:0.214266:0.327456:0.206091:0.327456:0.000000 5 1:@0.224535:0.353294:0.256046:0.353294:0.256046:0.339049:0.224535:0.339049:0.000000:0.000000:0.000000 6:@0.240751:0.365238:0.248926:0.365238:0.248926:0.350993:0.240751:0.350993:0.000000 7:@0.252830:0.377183:0.261005:0.377183:0.261005:0.362938:0.252830:0.362938:0.000000 8:@0.268309:0.389454:0.276484:0.389454:0.276484:0.375209:0.268309:0.375209:0.000000 15:@0.210178:0.365238:0.226528:0.365238:0.226528:0.350993:0.210178:0.350993:0.000000:0.000000 21:@0.224233:0.377183:0.240584:0.377183:0.240584:0.362938:0.224233:0.362938:0.000000:0.000000 28:@0.240584:0.389454:0.256934:0.389454:0.256934:0.375209:0.240584:0.375209:0.000000:0.000000 56:@0.210195:0.389454:0.226545:0.389454:0.226545:0.375209:0.210195:0.375209:0.000000:0.000000 1:@0.232425:0.341702:0.240600:0.341702:0.240600:0.327456:0.232425:0.327456:0.000000 1:@0.220481:0.331015:0.228656:0.331015:0.228656:0.316769:0.220481:0.316769:0.000000 M.4.1.33.:@0.096138:0.935208:0.142048:0.935208:0.142048:0.924453:0.096138:0.924453:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Reconocer y calcular productos notables e identificar factores de expresiones algebraicas.:@0.142048:0.935208:0.561224:0.935208:0.561224:0.925236:0.142048:0.925236:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 −:@0.494002:0.209749:0.500831:0.209749:0.500831:0.199238:0.494002:0.199238:0.000000 +:@0.522449:0.209749:0.529278:0.209749:0.529278:0.199238:0.522449:0.199238:0.000000 x:@0.481427:0.209292:0.486464:0.209292:0.486464:0.198248:0.481427:0.198248:0.000000 x:@0.514787:0.209292:0.519825:0.209292:0.519825:0.198248:0.514787:0.198248:0.000000 4:@0.474001:0.209292:0.480071:0.209292:0.480071:0.198715:0.474001:0.198715:0.000000 12:@0.501913:0.209292:0.513929:0.209292:0.513929:0.198715:0.501913:0.198715:0.000000:0.000000 9:@0.531144:0.209292:0.537214:0.209292:0.537214:0.198715:0.531144:0.198715:0.000000 2:@0.487571:0.204120:0.491089:0.204120:0.491089:0.197990:0.487571:0.197990:0.000000 +:@0.762479:0.209749:0.723795:0.209749:0.723795:0.199238:0.762479:0.199238:0.000000 +:@0.807993:0.209749:0.769308:0.209749:0.769308:0.199238:0.807993:0.199238:0.000000 +:@0.854289:0.209749:0.861118:0.209749:0.861118:0.199238:0.854289:0.199238:0.000000 a:@0.749556:0.209292:0.755812:0.209292:0.755812:0.198248:0.749556:0.198248:0.000000 a 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3:@0.886369:0.204120:0.889887:0.204120:0.889887:0.197990:0.886369:0.197990:0.000000