Question

How do you factor $x^2-y^2$?

Answer 1

Factorize using the algebraic identities

According to the identity of difference of two squares,

${\mathrm{a}}^{\mathrm{2}}\mathrm{-}{\mathrm{b}}^{\mathrm{2}}\mathrm{}\mathrm{=}\mathrm{}\left(a-b\right)\left(a+b\right)$

The given expression is $x^2-y^2$.

It can be factorized as follows,

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

$\Rightarrow x^2-y^2=\left(x-y\right)\left(x+y\right)$

Hence, the factors of $x^2-y^2$ obtained by using algebraic identity is $\left(x-y\right)\left(x+y\right)$.