This document provides instructions for factoring perfect square trinomials. It explains that a trinomial is a perfect square if the first and last terms are perfect squares and twice the product of the square roots of the first and last terms equals the middle term. The factored form of a perfect square trinomial is (a+b)^2 or (a-b)^2. It provides steps to follow which are: 1) take the square root of the first term, 2) take the square root of the last term, 3) express the result as the square of a binomial. It includes three examples showing the factoring of perfect square trinomials.

1. FACTORING PERFECT
SQUARE TRINOMIALS
MODULE 2
𝒂 𝟐
+ 𝟐𝒂𝒃 + 𝒃 𝟐
= 𝒂 + 𝒃 𝟐
𝒂 𝟐
− 𝟐𝒂𝒃 + 𝒃 𝟐
= 𝒂 − 𝒃 𝟐

2. How to factor a perfect square trinomial?
A trinomial is a perfect square trinomial if:
•The first and last terms are perfect
squares, and
•Twice the product of the square root of
the first and the last term is equal to the
middle term.

3. The factored form of a Perfect Square
Trinomial is represented by either of the
following:
𝒂 𝟐
+ 𝟐𝒂𝒃 + 𝒃 𝟐
= 𝒂 + 𝒃 𝟐
𝒂 𝟐
− 𝟐𝒂𝒃 + 𝒃 𝟐
= 𝒂 − 𝒃 𝟐

4. STEPS TO FOLLOW IN FACTORING PERFECT
SQUARE TRINOMIALS
1. Get the square root of the first term.
2. Get the square root of the last term.
3. Express the result as the square of a
binomial.

5. 𝒂 𝟐
+ 𝟐𝒂𝒃 + 𝒃 𝟐
𝒙 𝟐
+ 𝟔𝒙 + 𝟗
𝒙 𝟐 = 𝒙
= 𝒂 + 𝒃 𝟐
𝟐 𝒙 𝟑
= 𝒙 + 𝟑 𝟐
𝟗 = 𝟑
𝒂 𝒃
= 𝟔𝒙
EXAMPLE 1:

6. 𝒂 𝟐
− 𝟐𝒂𝒃 + 𝒃 𝟐
𝟒𝒎 𝟐 − 𝟐𝟎𝒎 + 𝟐𝟓
𝟒𝒎 𝟐 = 𝟐𝒎
= 𝒂 − 𝒃 𝟐
𝟐 𝟐𝒎 𝟓
= 𝟐𝒎 − 𝟓 𝟐
𝟐𝟓 = 𝟓
𝒂 𝒃
= 𝟐𝟎𝒎
EXAMPLE 2:

7. 𝒂 𝟐
+ 𝟐𝒂𝒃 + 𝒃 𝟐
𝒙 𝟐
+ 𝟒𝒙 + 𝟏𝟔
𝒙 𝟐 = 𝒙
𝟐 𝒙 𝟒
∴ The given equation is not a Perfect Square Trinomial
𝟏𝟔 = 𝟒
𝒂 𝒃
= 𝟖𝒙
EXAMPLE 3:
𝟒𝒙 ≠ 𝟖𝒙