# 4.5 Factoring a Perfect Square Trinomial

A perfect square trinomial is a trinomial that can be written as the square of a binomial. Recall that when a binomial is squared, the result is the square of the first term added to twice the product of the two terms and the square of the last term.

## Perfect Square Trinomials

A perfect square trinomial can be written as the square of a binomial:

${a}^{2}+2ab+{b}^{2}={(a+b)}^{2}$

## How To

**Given a perfect square trinomial, factor it into the square of a binomial.**

- Confirm that the first and last term are perfect squares.
- Confirm that the middle term is twice the product of [latex]ab[/latex].
- Write the factored form as [latex](a+b)^2[/latex].

## Example 1: Factoring a Perfect Square Trinomial

- Factor [latex]25x^2 + 20x + 4[/latex].
- Factor [latex]49x^2−14x+1[/latex].

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