Question

help me tofactorise​

Answer 1

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

Identity used is :

${(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ca$

Where,

$a = - \sqrt{2} x$

$b = y$

$c = 2 \sqrt{2} z$