1. Lesson 9.5: Factoring Difference of Squares, page 500
Objectives:
To factor binomials that are the difference of squares.
To solve equations involving the differences of squares.

2. Review of 9.3 & 9.4 Define factoring.
How do we check our answer after factoring?
Factor:
A) k2 – 11kh + 28h2 B) 4x2 + 2x - 6

3. DIFFERENCE OF TWO SQUARES
Review
Multiply using FOIL: (x – 3) (x + 3).
x2 + 3x – 3x - 9
Answer: x2 – 9
Remember: the outside/inside terms cancel b/c they are opposite terms.
Multiply: (y + 2)(y – 2)
Answer: y2 – 4
This answer is a special case called the
DIFFERENCE OF TWO SQUARES
(a.k.a. DOTS).

4. Factoring the Difference of Two Squares (DOTS)
Clue 1: usually only 2 terms
Clue 2: minus sign
Clue 3: both terms are perfect squares
General Form: x2 – y2 = (x + y)(x - y)
MEMORIZE THESE PERFECT SQUARES:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256,…, 400,…,625,…900,…,10000

5. Example 1: Factor each binomial. x2 – y2 = (x + y)(x - y)
a) x2 – 25 b) 3a2 – 48
c) 169x2 – y2 d) 81a2 – 121b2
Note: Always check for the GCF.

6. m² - 64
3b³ - 27b
g) 16y² - 81z² h)

7. Ex. 2: Apply several different factoring techniques.
1. 6x³ + 30x² - 24x - 120

8. Ex. 3: Solve equations by factoring.
– 68k² = 0

9. 3.
a = 49a³

10. Review Examples Factor Completely
4x2 – 12x
12q2b +8qb2 – 20q3b2
2am – 2bm – ap + bp
y2 – 5y + 6
10k2 – 11kh + 3h2
64m2 – 25n2

11. SUMMARY
x2 – y2 = (x + y)(x - y)
NBA #5, page 505, problems even