Perfect Square Trinomials

To identify a Perfect Square Trinomial:

• The first and last terms are positive.
• The middle term is 2 times the product of the outer terms.

Your factoring will look something like this:

When the middle term is positive: a2 + 2ab + b2 = (a+b)2

When the middle term is negative: a2 - 2ab + b2 = (a-b)2

Example: 4x2 + 36x + 81

1. Take the square root of the two outer terms.
Square root of 4x2 = 2x Square root of 81 = 9

2. Multiple these terms together, then multiple by 2

(2x * 9) = 18x (* 2) = 36x [This should equal the middle term from your original equation]

3a. Since the middle term is positive, the sign in your equation will be positive as well.

4x2 + 36x + 81 = (2x + 9)2

3b. If the middle term is negative, then your sign would be negative, too.

4x2 - 36x + 81 = (2x - 9)2




Here's another example: 4x2 + 12x + 9

Square root of 4x2= 2x Square root of 9 = 3

(2x * 3)

6x (* 2)

12x

(Since your sign is positive...)

4x2 + 12x + 9 = (2x + 3) 2