Question

Factorise the following: $x^4-13x^2{y}^2+36y^4$

Answer 1

Given: $x^4-13x^2{y}^2+36y^4$

$=x^4-9x^2{y}^2-4x^2{y}^2+36y^4$, (split the middle term)

$=(x^4-9x^2{y}^2)+(-4x^2{y}^2+36y^4)$, (group pair of terms)

$=x^2(x^2-9y^2)-4y^2(x^2-9y^2)$, (factor each binomials)

$=(x^2-9y^2)(x^2-4y^2)$, (factor out common factor $(x^2-9y^2)$)

$=(x+3y)(x-3y)(x+2y)(x-2y)$, (since $a^2-b^2=(a+b)(a-b)$)