Solución
desarrollar (164x+165y+163z+164w)4
Solución
409616x4+16w4+16x2w2+25x2y2+9x2z2+32x3w+32xw3+16w2x2+25w2y2+9w2z2+40x3y+24x3z+40yw3+24zw3+125xy3+125y3w+27xz3+27z3w+50xy2w+18xz2w+40x2yw+24x2zw+40xyw2+24xzw2+225xy2z+225y2zw+135xyz2+135yz2w+65536625y4+400y2x2+400y2w2+225y2z2+750y3z+270yz3+81z4+144z2x2+144z2w2+225z2y2+480x2yz+480yzw2+5125x3y+3x3z+5yw3+3zw3+25xyw2+15xzw2+25x2yw+15x2zw+204825y2x2+25y2w2+9z2x2+9z2w2+25x2y2+9x2z2+25w2y2+9w2z2+75x2yz+75yzw2+125xy2w+45xz2w+180xyzw+128(x2w+xw2)x+(x2w+xw2)w+327685(75y2z+45yz2)y+3(75y2z+45yz2)z
Pasos de solución
(164x+165y+163z+164w)4
Simplificar (164x+165y+163z+164w)4:(164x+165y+163z+164w)(164x+165y+163z+164w)(164x+165y+163z+164w)(164x+165y+163z+164w)
=(164x+165y+163z+164w)(164x+165y+163z+164w)(164x+165y+163z+164w)(164x+165y+163z+164w)
Desarrollar (164x+165y+163z+164w)(164x+165y+163z+164w):25616x2+16w2+25y2+9z2+325xy+3xz+5yw+3zw+8xw+12815yz
=(25616x2+16w2+25y2+9z2+325xy+3xz+5yw+3zw+8xw+12815yz)(164x+165y+163z+164w)(164x+165y+163z+164w)
Desarrollar (25616x2+16w2+25y2+9z2+325xy+3xz+5yw+3zw+8xw+12815yz)(164x+165y+163z+164w):1024(16x2+16w2+25y2+9z2)x+(16x2+16w2+25y2+9z2)w+40965(16x2+16w2+25y2+9z2)y+3(16x2+16w2+25y2+9z2)z+1285x2y+3x2z+5yw2+3zw2+15xyw+9xzw+51225xy2+25y2w+9xz2+9z2w+45xyz+45yzw+32x2w+xw2+204875y2z+45yz2
=(1024(16x2+16w2+25y2+9z2)x+(16x2+16w2+25y2+9z2)w+40965(16x2+16w2+25y2+9z2)y+3(16x2+16w2+25y2+9z2)z+1285x2y+3x2z+5yw2+3zw2+15xyw+9xzw+51225xy2+25y2w+9xz2+9z2w+45xyz+45yzw+32x2w+xw2+204875y2z+45yz2)(164x+165y+163z+164w)
Aplicar la siguiente regla de productos notables=1024(16x2+16w2+25y2+9z2)x+(16x2+16w2+25y2+9z2)w164x+1024(16x2+16w2+25y2+9z2)x+(16x2+16w2+25y2+9z2)w165y+1024(16x2+16w2+25y2+9z2)x+(16x2+16w2+25y2+9z2)w163z+1024(16x2+16w2+25y2+9z2)x+(16x2+16w2+25y2+9z2)w164w+40965(16x2+16w2+25y2+9z2)y+3(16x2+16w2+25y2+9z2)z164x+40965(16x2+16w2+25y2+9z2)y+3(16x2+16w2+25y2+9z2)z165y+40965(16x2+16w2+25y2+9z2)y+3(16x2+16w2+25y2+9z2)z163z+40965(16x2+16w2+25y2+9z2)y+3(16x2+16w2+25y2+9z2)z164w+1285x2y+3x2z+5yw2+3zw2+15xyw+9xzw164x+1285x2y+3x2z+5yw2+3zw2+15xyw+9xzw165y+1285x2y+3x2z+5yw2+3zw2+15xyw+9xzw163z+1285x2y+3x2z+5yw2+3zw2+15xyw+9xzw164w+51225xy2+25y2w+9xz2+9z2w+45xyz+45yzw164x+51225xy2+25y2w+9xz2+9z2w+45xyz+45yzw165y+51225xy2+25y2w+9xz2+9z2w+45xyz+45yzw163z+51225xy2+25y2w+9xz2+9z2w+45xyz+45yzw164w+32x2w+xw2164x+32x2w+xw2165y+32x2w+xw2163z+32x2w+xw2164w+204875y2z+45yz2164x+204875y2z+45yz2165y+204875y2z+45yz2163z+204875y2z+45yz2164w
Simplificar 1024(16x2+16w2+25y2+9z2)x+(16x2+16w2+25y2+9z2)w164x+1024(16x2+16w2+25y2+9z2)x+(16x2+16w2+25y2+9z2)w165y+1024(16x2+16w2+25y2+9z2)x+(16x2+16w2+25y2+9z2)w163z+1024(16x2+16w2+25y2+9z2)x+(16x2+16w2+25y2+9z2)w164w+40965(16x2+16w2+25y2+9z2)y+3(16x2+16w2+25y2+9z2)z164x+40965(16x2+16w2+25y2+9z2)y+3(16x2+16w2+25y2+9z2)z165y+40965(16x2+16w2+25y2+9z2)y+3(16x2+16w2+25y2+9z2)z163z+40965(16x2+16w2+25y2+9z2)y+3(16x2+16w2+25y2+9z2)z164w+1285x2y+3x2z+5yw2+3zw2+15xyw+9xzw164x+1285x2y+3x2z+5yw2+3zw2+15xyw+9xzw165y+1285x2y+3x2z+5yw2+3zw2+15xyw+9xzw163z+1285x2y+3x2z+5yw2+3zw2+15xyw+9xzw164w+51225xy2+25y2w+9xz2+9z2w+45xyz+45yzw164x+51225xy2+25y2w+9xz2+9z2w+45xyz+45yzw165y+51225xy2+25y2w+9xz2+9z2w+45xyz+45yzw163z+51225xy2+25y2w+9xz2+9z2w+45xyz+45yzw164w+32x2w+xw2164x+32x2w+xw2165y+32x2w+xw2163z+32x2w+xw2164w+204875y2z+45yz2164x+204875y2z+45yz2165y+204875y2z+45yz2163z+204875y2z+45yz2164w:409616x4+16w4+16x2w2+25x2y2+9x2z2+32x3w+32xw3+16w2x2+25w2y2+9w2z2+40x3y+24x3z+40yw3+24zw3+125xy3+125y3w+27xz3+27z3w+50xy2w+18xz2w+40x2yw+24x2zw+40xyw2+24xzw2+225xy2z+225y2zw+135xyz2+135yz2w+65536625y4+400y2x2+400y2w2+225y2z2+750y3z+270yz3+81z4+144z2x2+144z2w2+225z2y2+480x2yz+480yzw2+5125x3y+3x3z+5yw3+3zw3+25xyw2+15xzw2+25x2yw+15x2zw+204825y2x2+25y2w2+9z2x2+9z2w2+25x2y2+9x2z2+25w2y2+9w2z2+75x2yz+75yzw2+125xy2w+45xz2w+180xyzw+128(x2w+xw2)x+(x2w+xw2)w+327685(75y2z+45yz2)y+3(75y2z+45yz2)z
=409616x4+16w4+16x2w2+25x2y2+9x2z2+32x3w+32xw3+16w2x2+25w2y2+9w2z2+40x3y+24x3z+40yw3+24zw3+125xy3+125y3w+27xz3+27z3w+50xy2w+18xz2w+40x2yw+24x2zw+40xyw2+24xzw2+225xy2z+225y2zw+135xyz2+135yz2w+65536625y4+400y2x2+400y2w2+225y2z2+750y3z+270yz3+81z4+144z2x2+144z2w2+225z2y2+480x2yz+480yzw2+5125x3y+3x3z+5yw3+3zw3+25xyw2+15xzw2+25x2yw+15x2zw+204825y2x2+25y2w2+9z2x2+9z2w2+25x2y2+9x2z2+25w2y2+9w2z2+75x2yz+75yzw2+125xy2w+45xz2w+180xyzw+128(x2w+xw2)x+(x2w+xw2)w+327685(75y2z+45yz2)y+3(75y2z+45yz2)z