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factorise 2x^2 +y^2 +8z^2-2sqrt(2)xy+4sq...

factorise `2x^2 +y^2 +8z^2-2sqrt(2)xy+4sqrt(2)yz-8xz`

Text Solution

Verified by Experts

We observe here that `2sqrt(2)xy and -8zx` are negative terms in the given expression and x occurs in both the terms.
So, we wire ` 2x^2 " as " (-sqrt(2x))^2`.
`therefore 2x^2+y^2+8z^2-2sqrt(2)xy+4sqrt(2)yz-8zx`
`=(-sqrt(2x))^2+y^2(2sqrt(2)z)^2+{2xx(-sqrt(2)x)xxy}+{2xxy xx (2sqrt(2)z)}+{2xx(2sqrt(2)z)xx(-sqrt(2)x)}`
`=(-sqrt(2)x+y+2sqrt(2)z)^2`.
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