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Question

What is formula for x-y-z3


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Solution

Expanding expression x-y-z3:

x-y-z3 can be rewritten as follows:

x-y-z3=x-y-z2(x-y-z)=x2+y2-2xy+z2-2xz+2yz(x-y-z)[(x+y+z)2=x2+y2+z2+2xy+2xz+2yz]=x3-y3-z3+xy2-2x2y+z2x-2x2z+2xyz-x2y+2xy2-z2y+2xyz-2y2z-x2z-y2z+2xyz+2xz2-2yz2=x3-y3-z3-3x2y+3xy2-3y2z-3yz2+3xz2-3x2z+6xyz.

Thus, the formula for (x-y-z)3 is.x3-y3-z3-3x2y+3xy2-3y2z-3yz2+3xz2-3x2z+6xyz


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