Question

Factorise :
$z^2-(x^2-2xy+y^2)$

Answer 1

$z^2(x^2-2xy+y^2)$

$\Rightarrow z^2-(x-y{)}^2$

$\left(\right(x-y{)}^2=x^2+y^2-2xy\left)\right(a^2-b^2=(a-b)(a+b))$

$\Rightarrow (z-(x-y\left)\right)(z+(x-y\left)\right)$

$\Rightarrow (z-x+y)(z+x-y)$

$\therefore \Rightarrow (-x+y+z)(x-y+z)$