Question

How do you factor $x^4-y^4$?

Answer 1

Find factors of the expression:

Given expression is $x^4-y^4$.

Rewrite the expression as follows,

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

Note that, $a^2-b^2=\left(a+b\right)\left(a-b\right)$.

so,

$\begin{array}{rcl}& \Rightarrow & {\left(x^2\right)}^2-{\left(y^2\right)}^2=\left(x^2+y^2\right)\left(x^2-y^2\right)\\ & =& \left(x^2+y^2\right)\left(x+y\right)\left(x-y\right)\end{array}$

Hence, the factors of the expression are $\begin{array}{l}\left(x^2+y^2\right)\left(x+y\right)\left(x-y\right).\end{array}$