Recall the formula to factor a difference of squares.
\begin{gathered}
\col{a}^2-\colII{b}^2 \quad \Leftrightarrow \quad (\col{a}+\colII{b})(\col{a}-\colII{b})
\end{gathered}
We can apply this formula to our expression.
\begin{gathered}
(\col{w^2})^2-\colII{25}^2 \quad \Leftrightarrow \quad (\col{w^2}+\colII{25})(\col{w^2}-\colII{25})
\end{gathered}
Now, let's take a look at the expression $w^2-25.$ Once again, we can express it as a difference of two perfect squares. Let's do it!
Now, we can apply the above formula to factor our expression completely.
\begin{gathered}
\left(w^2+25^2\right)\left(\col{w}^2-\colII{5}^2\right) \\
\Updownarrow \\
\left(w^2+25\right)\left(\col{w}+\colII{5}\right)\left(\col{w}-\colII{5}\right)
\end{gathered}
Checking Our Answer
Check your answer $\checkmark$
We can apply the Distributive Property and compare the result with the given expression.
After applying the Distributive Property and simplifying, the result is the same as the given expression. Therefore, we can be sure our solution is correct!
