Factorise

$2 straight x squared plus straight y squared plus 8 straight z squared minus 2 square root of 2 xy plus 4 square root of 2 yz minus 8 zx$

Solution

2 straight x squared plus straight y squared plus 8 straight z squared minus 2 square root of 2 xy plus 4 square root of 2 yz minus 8 zx 2 straight x squared plus straight y squared plus 8 straight z squared minus 2 square root of 2 xy plus 4 square root of 2 yz minus 8 zx equals space open parentheses negative square root of 2 straight x close parentheses squared plus straight y squared plus open parentheses 2 square root of 2 straight z close parentheses squared plus 2 open parentheses negative square root of 2 straight x close parentheses straight y plus 2 straight y open parentheses 2 square root of 2 straight z close parentheses plus 2 open parentheses 2 square root of 2 straight z close parentheses left parenthesis negative square root of 2 straight z end root right parenthesis equals space left parenthesis negative square root of 2 straight x plus straight y plus 2 square root of 2 straight z end root right parenthesis squared equals space left parenthesis negative square root of 2 straight x end root plus straight y plus 2 square root of 2 straight z end root right parenthesis space left parenthesis negative square root of 2 straight x end root plus straight y plus 2 square root of 2 straight x right parenthesis.

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