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Question
Simplify:
(x + 2y + 3z)(x2 + 4y2 + 9z2 - 2xy - 6yz - 3zx)
Solution
(x + 2y + 3z)(x2 + 4y2 + 9z2 - 2xy - 6yz - 3zx)
= x(x2 + 4y2 + 9z2 - 2xy - 6yz - 3zx) + 2y(x2 + 4y2 + 9z2 - 2xy - 6yz - 3zx)
= x3 + 4xy2 + 9xz2 - 2x2y - 6xyz - 3zx2 + 2x2y + 8y3 + 18yz2 - 4xy2 - 122z - 6xyz + 3x2z + 12y2z + 27z3 - 6xyz - 18yz2 - 9xz2
= x3 + 8y3 + 27z3 - 18xyz.
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