Question

Factorise: $x^4-2x^2{y}^2+y^4$

Answer 1

We need to factorise $x^4-2x^2{y}^2+y^4$

$x^4-2x^2{y}^2+y^4$ $=x^4-x^2{y}^2-x^2{y}^2+y^4$

$=x^2(x^2-y^2)-y^2(x^2-y^2)$

$=(x^2-y^2{)}^2$

$=(x^2-y^2)(x^2-y^2)$

Now by using identity $a^2-b^2=(a+b)(a-b)$

Thus factors are $(x-y)(x+y)(x-y)(x+y)$.