Examples

Factor the difference of squares:

Example 1

\(\begin{align*}x^4 - 25\end{align*}\)

Rewrite \(\begin{align*}x^4 - 25\end{align*}\) as \(\begin{align*}(x^2)^2 - 5^2\end{align*}\). This factors as \(\begin{align*}(x^2 + 5)(x^2 - 5)\end{align*}\).

Example 2

\(\begin{align*}16x^4 - y^2\end{align*}\)

Rewrite \(\begin{align*}16x^4 - y^2\end{align*}\) as \(\begin{align*}(4x^2)^2 - y^2\end{align*}\). This factors as \(\begin{align*}(4x^2 + y)(4x^2 - y)\end{align*}\).

Example 3

\(\begin{align*}x^2 y^8 - 64z^2\end{align*}\)

Rewrite \(\begin{align*}x^2 y^4 - 64z^2\end{align*}\) as \(\begin{align*}(xy^2)^2 - (8z)^2\end{align*}\). This factors as \(\begin{align*}(xy^2 + 8z)(xy^2 - 8z)\end{align*}\).