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Question
Multiply x2 + 4y2 + z2 + 2xy + xz – 2yz by (–z + x – 2y).
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Solution
According to the question:
(x2 + 4y2 + z2 + 2xy + xz – 2yz) × (–z + x – 2y)
Now, multiply as follows:
= {x + (–2y) + (–z)}{(x)2 + (–2y)2 + (–z2) – (x)(–2y) – (–2y)(–z) – (–z)(x)}
= x3 + (–2y)3 + (–z)3 – 3 × x × (–2y) × (–z)
Use the identity:
(a + b + c)(a2 + b2 + c2 – ab – bc – ca) = a3 + b3 + c3 – 3abc
= x3 – 8y3 – z3 – 6xyz
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