Unit 1 – Lesson 3: Factoring Perfect Square Trinomials
Vocabulary
“Perfect Square”
Examples:




1
2
3
4
×
×
×
×
1
2
3
4
=
=
=
=
1²
2²
3²
4²
=
=
=
=
1
4
9
16
Therefore: 1, 4, 9, 16 are Perfect Squares
Another example:

(x) × (x) = x²
Therefore: x² is a Perfect Square
-4x²
Terms: 5x², x, - 3x
4
Constant Term: - 3, 7 , 24
Monomial: 4x
Binomial: 3x + 3
Trinomial: x² - 2x + 6
Let’s assume that a and b are terms:
“Perfect Square Trinomials”
(a + b)(a + b) = (a + b)² = a² + 2ab +b²
Example Question: Expand and simplify
(x + 2)² =
(a – b)(a – b) = (a – b)² = a² - 2ab + b²
Example Question: Expand and simplify
(x – 3)² =
How to Factor a Perfect Square Trinomial
Step 1: Make sure it’s a perfect square trinomial



First and last term are perfect squares
Find the value of a and b
Middle term is 2 × a × b
Step 2: If middle term is negative, then use (a – b)²
If middle term is positive, then use (a + b)²
Example Question: Factor the following perfect square trinomials
a)
x² - 8x + 16 =
b)
x² + 25x + 25 =
Practice Questions: Factor the following. (Note: not all of them are perfect square trinomials)
a) x² - 6x + 12
b) x² - 12x + 36
c) 4n² + 12n + 9