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

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

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

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

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)

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

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

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

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

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

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

Warm Up Solve 64 𝑥 2 =49

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

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

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

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

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

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)

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)