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Question
Expand the following, using suitable identity:
(x + 2y + 4z)2
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Solution
It is known that,
(x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx
(x + 2y + 4z)2 = x2 + (2y)2 + (4z)2 + 2(x)(2y) + 2(2y)(4z) + 2(4z)(x)
= x2 + 4y2 + 16z2 + 4xy + 16yz + 8xz
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