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Question
Expand x2(x + y + z) + y2(x + y + z) + z2(x – y – z)
Solution
x2(x + y + z) + y2(x + y + z) + z2(x – y – z) = (x2 × x) + (x2 × y) + (x2 × z) + (y2 × x) + (y2 × y) + (y2 × z) + (z2 × x) + z2 (– y) + z2 (– z)
= x3 + x2y + x2z + xy2 + y3 + y2z + xz2 – yz2 – z3
= x3 + y3 – z3 + x2y + x2z + xy2 + zy2 + xz2 – yz2
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