Question

Factorize $x^4-y^4$ by using identity $a^2-b^2=(a+b)(a-b)$.

Answer 1

Factorize the given polynomial

Given: $x^4-y^4={\left(x^2\right)}^2-{\left(y^2\right)}^2$

use the identity $a^2-b^2=(a+b)(a-b)$

$x^4-y^4=(x^2-y^2)(x^2+y^2)$

Again using the identity $a^2-b^2=(a+b)(a-b)$

$x^4-y^4=(x-y)(x+y)(x^2+y^2)$

Hence, the factorized form of the polynomial $x^4-y^4$ is $(x-y)(x+y)$$(x^2+y^2)$.