Question

FACTORISE this please answer with explaination ​

Answer 1

$2x^{2}+y^{2}+8z^{2}-2\sqrt{2}xy+4\sqrt{2}yz-8xz$

$= (-\sqrt{2}x)^{2} + y^{2}+(2\sqrt{2}z)^{2} +2\times(-\sqrt{2}x)\times y + 2\times y\times(2\sqrt{2}y) + 2\times (2\sqrt{2}y)\times(-\sqrt{2}x)$

$= ( -\sqrt{2}x + y + 2\sqrt{2}z )^{2}$

$= ( -\sqrt{2}x + y + 2\sqrt{2}z )( -\sqrt{2}x + y + 2\sqrt{2}z )$

Therefore.,

$\red {2x^{2}+y^{2}+8z^{2}-2\sqrt{2}xy+4\sqrt{2}yz-8xz }$

$\green {= ( -\sqrt{2}x + y + 2\sqrt{2}z )( -\sqrt{2}x + y + 2\sqrt{2}z )}$

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