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Question
Simplify: (x – 2y + 3z) (x2 + 4y2 + 9z2 + 2xy + 6yz – 3xz)
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Solution
(x – 2y + 3z) (x2 + 4y2 + 9z2 + 2xy + 6yz – 3xz)
(a + b + c) (a2 + b2 + c2 – ab – bc – ca) = a3 + b3 + c3 – 3abc .
∴ (x – 2y + 3z) (x2 + 4y2 + 9z2 + 2xy + 6yz – 3xz)
= x3 + (–2y)3 + (3z)3 – 3(x)(–2y)(3z)
= x3 – 8y3 + 27z3 + 18xyz
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