1. Section 8.8-8.9 Day 1 Difference of Squares Perfect Square Trinomials
Algebra 1

2. Learning Targets Factor binomials that are the difference of squares
Use the difference of squares to solve equations
Write a perfect square trinomial as a single binomial factor with a square exponent
Factor by grouping

3. Recall
Given 𝑥 2 −4, what do you think the initial 2 binomials were? (___±___)(___±___)= 𝑥 2 −4 Answer: (𝑥+2)(𝑥−2)

4. Recall
Given 16 𝑥 2 −9, what do you think the initial 2 binomials were? (___±___)(___±___)=16 𝑥 2 −9 Answer: (4𝑥+3)(4𝑥−3)

5. Recall
Given 25 𝑎 2 −81 𝑏 2 , what do you think the initial 2 binomials were? (___±___)(___±___)=25 𝑎 2 −81 𝑏 2 Answer: (5𝑎+9𝑏)(5𝑎−9𝑏)

6. Difference of Squares
𝑎 2 − 𝑏 2 =(𝑎+𝑏)(𝑎−𝑏) In this case, 𝑏=0. Thus, 𝑎 𝑥 2 +𝑏𝑥−𝑐=𝑎 𝑥 2 −𝑐

7. Factor: Example 1
Factor 121−4 𝑏 2
A = 11
B = 2b
(11+2𝑏)(11−2𝑏)

8. Factor: Example 2
Factor 𝑥 2 −81
A = x
B = 9
(𝑥+9)(𝑥−9)

9. Factor: Example 3
Factor 49 𝑥 2 −16
A = 7
B = 4
(7𝑥−4)(7𝑥+4)

10. Factor: Example 4
Factor 16 ℎ 2 −9 𝑎 2
A = 4h
B = 3a
4ℎ+3𝑎 (4ℎ−3𝑎)

11. Factor: Example 5
Factor 64 𝑔 2 − ℎ 2
A = 8g
B = h
(8𝑔+ℎ)(8𝑔−ℎ)

12. Warm Up
Solve 64 𝑥 2 =49

13. Perfect Square Trinomials
𝑎 2 ±2𝑎𝑏+ 𝑏 2 𝑎+𝑏 2 =(𝑎+𝑏)(𝑎+𝑏) Or 𝑎−𝑏 2 =(𝑎−𝑏)(𝑎−𝑏)

14. Factor Perfect Squares: Ex 1
AC = 36, B = 12
2 numbers: 6, 6
4𝑦+6 4𝑦+6 = 2𝑦+3 2𝑦+3 = 2𝑦+3 2

15. Factor Perfect Squares: Ex 2
AC = 9, B = -6
2 numbers: −3, −3
𝑥−3 𝑥−3 = 𝑥−3 2

16. Factor Perfect Squares: Ex 3
Solve 9 𝑥 2 −12𝑥=−4
AC = 36, B= -12
2 numbers: −6, −6
9𝑥−6 9𝑥−6 = 3𝑥−2 3𝑥−2 = 3𝑥−2 2
𝑥= 2 3

17. Factor Perfect Squares: Ex 4
AC = 16, B = 8
2 numbers: 4, 4
𝑥+4 𝑥+4 = 𝑥+4 2

18. Example 1: GCF/Difference of Squares
Factor 27 𝑔 3 −3𝑔.
Hint (Take out GCF first)
2𝑔(9 𝑔 2 −1)
A=3g
B=1
2𝑔(3𝑔+1)(3𝑔−1)

19. Example 2: GCF/Difference of Squares
Factor 9 𝑥 3 −4𝑥.
Hint: (Take out GCF first)
𝑥(9 𝑥 2 −4)
A= 3x
B= 2
𝑥(3𝑥+2)(3𝑥−2)