Question

Factorise 2x²+8y²+z²-8xy-4√2yz+2√2zx

Answer 1

$2 {x}^{2} + 8 {y}^{2} + {z}^{2} - 8xy - 4 \sqrt{2} yz + 2 \sqrt{2} zx \\ \\ { (\sqrt{2} x)}^{2} +( - 2 \sqrt{2} y) {}^{2} + {z}^{2} + 2.( \sqrt{2}x).( - 2 \sqrt{2} y ) + 2.( - 2 \sqrt{2} y).(z) + 2. (\sqrt{2} x).z \\ \\ {( \sqrt{2} x - 2 \sqrt{2y} + z )}^{2} \: \: \\ \\ \bold{or} \\ \\2 {x}^{2} + 8 {y}^{2} + {z}^{2} - 8xy - 4 \sqrt{2} yz + 2 \sqrt{2} zx \\ \\ { ( - \sqrt{2} x)}^{2} +( 2 \sqrt{2} y) {}^{2} + {( - z)}^{2} + 2.( - \sqrt{2}x).( 2 \sqrt{2} y ) + 2.( 2 \sqrt{2} y).( - z) + 2. ( - \sqrt{2} x).( - z) \\ \\ ( - \sqrt{2} x + 2 \sqrt{2} y - z) {}^{2}$

Hence, Solved.