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.
We can use this equation to factor any perfect square trinomial.
Perfect Square Trinomials
A perfect square trinomial can be written as the square of a binomial:
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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