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Question
Factorise:
`2x^2 + y^2 + 8z^2 - 2sqrt2xy + 4sqrt2yz - 8xz`
Solution
It is known that,
(x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx
`2x^2 + y^2 + 8z^2 - 2sqrt2xy + 4sqrt2yz - 8xz`
= `(-sqrt2x)^2 + (y)^2 + (2sqrt2z)^2 + 2(-sqrt2x)(y) + 2(y)(2sqrt2z) + 2(-sqrt2x)(2sqrt2z)`
= `(-sqrt2x + y + 2sqrt2z)^2`
= `(-sqrt2x + y + 2sqrt2z)(-sqrt2x + y + 2sqrt2z)`
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