1. Section 9.7 “Factor Special Products”
(1) perfect square trinomials
(2) the difference of two squares
Squares are numbers or variables that have a
whole number or whole variable square root. x² 9 t² 1 25
4z²

2. Section 9.7 “Factor Special Products”
You can use the following special products patterns to help you factor certain polynomials.
Perfect Square Trinomial Pattern (addition)
a² + 2ab + b²
(a + b)²
(a + b)(a + b)
Perfect Square Trinomial Pattern (subtraction)
a² – 2ab + b²
(a – b)²
(a - b)(a - b)
Difference of Two Squares Pattern
a² – b²
(a + b)(a – b)

3. a² + 2ab + b² (a + b)² (x + 5)² x² + 10x + 25 (3x + 2)² 9x² + 12x + 4
Perfect Square Trinomial Pattern (addition)
a² + 2ab + b²
(a + b)²
(a + b)(a + b)
Always check for perfect squares FIRST!!
(x + 5)²
x² + 10x + 25
(3x + 2)²
9x² + 12x + 4
2(3x + 2)²
2(9x² + 12x + 4)
18x² + 24x + 8
Factor out 2 first, then look for perfect squares.

4. a² – 2ab + b² (a – b)² (x – 3)² x² – 6x + 9 (6y – 1)² 36y² – 12y + 1
Perfect Square Trinomial Pattern (subtraction)
a² – 2ab + b²
(a – b)²
(a - b)(a - b)
Always check for perfect squares FIRST!!
(x – 3)²
x² – 6x + 9
(6y – 1)²
36y² – 12y + 1
3(x² – 2xy + y²)
3x² – 6xy + 3y²
3(x – y)²
Factor out 3 first, then look for perfect squares.

5. a² – b² (a + b)(a – b) x² – 16 (x + 4)(x – 4) 9(2y + 3)(2y – 3)
Difference of Two Squares Pattern
a² – b²
(a + b)(a – b)
Always check for perfect squares FIRST!!
x² – 16
(x + 4)(x – 4)
9(2y + 3)(2y – 3)
36y² – 81
(7c + d)(7c – d)
49c² – d²