(x+y+z)^3 = ?
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(x+y+z)^3
=(x+y+z)*(x+y+z)*(x+y+z)
=(x+y+z)(x2+2xy+2xz+y2+2yz+z2)
=(x)(x2)+(x)(2xy)+(x)(2xz)+(x)(y2)+(x)(2yz)+(x)(z2)+(y)(x2)+(y)(2xy)+(y)(2xz)+(y)(y2)+(y)(2yz)+(y)(z2)+(z)(x2)+(z)(2xy)+(z)(2xz)+(z)(y2)+(z)(2yz)+(z)(z2)
=x3+2x2y+2x2z+xy2+2xyz+xz2+x2y+2xy2+2xyz+y3+2y2z+yz2+x2z+2xyz+2xz2+y2z+2yz2+z3
=x3+3x2y+3x2z+3xy2+6xyz+3xz2+y3+3y2z+3yz2+z3
=(x+y+z)*(x+y+z)*(x+y+z)
=(x+y+z)(x2+2xy+2xz+y2+2yz+z2)
=(x)(x2)+(x)(2xy)+(x)(2xz)+(x)(y2)+(x)(2yz)+(x)(z2)+(y)(x2)+(y)(2xy)+(y)(2xz)+(y)(y2)+(y)(2yz)+(y)(z2)+(z)(x2)+(z)(2xy)+(z)(2xz)+(z)(y2)+(z)(2yz)+(z)(z2)
=x3+2x2y+2x2z+xy2+2xyz+xz2+x2y+2xy2+2xyz+y3+2y2z+yz2+x2z+2xyz+2xz2+y2z+2yz2+z3
=x3+3x2y+3x2z+3xy2+6xyz+3xz2+y3+3y2z+3yz2+z3
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