Factoring Using Perfect Square Trinomials

We use the square of a binomial formula to factor perfect square trinomials. A perfect square trinomial has the form \(\begin{align*}a^2 + 2ab + b^2\end{align*}\) or \(\begin{align*}a^2 - 2ab + b^2\end{align*}\).

In these special kinds of trinomials, the first and last terms are perfect squares and the middle term is twice the product of the square roots of the first and last terms. In a case like this, the polynomial factors into perfect squares:

\(\begin{align*}a^2 + 2ab + b^2 & = (a + b)^2\\ a^2 - 2ab + b^2 & = (a - b)^2\end{align*}\)

Once again, the key is figuring out what the \(\begin{align*}a\end{align*}\) and \(\begin{align*}b\end{align*}\) terms are.

Source: cK-12, https://www.ck12.org/algebra/factor-perfect-square-trinomials/lesson/Factorization-using-Perfect-Square-Trinomials-ALG-I/
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