Question

Factorise:
$2x^2+y^2+8z^2–2\sqrt{2}xy+4\sqrt{2}yz–8xz$ [3 MARKS]

Answer 1

Formula: 1 Mark
Factorisation: 2 Marks

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

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

$=(-\sqrt{2}x{)}^2+y^2+(2\sqrt{2}z{)}^2+2(-\sqrt{2}x)\left(y\right)+2\left(y\right)\left(2\sqrt{2}z\right)+2(-\sqrt{2}x)\left(2\sqrt{2}z\right).....\left(i\right)$

${(x+y+z)}^2=x^2+y^2+z^2+2xy+2yz+2zx$
[Comparing equation (i) from above identity, we get]

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

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