1. Section 8.8-8.9 Day 2 Difference of Squares Perfect Square Trinomials Factor by Grouping
Algebra 1

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)

3. 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)

4. Example 3: GCF/Difference of Squares
Solve 25 𝑑 3 −49𝑑=0
1. Factor GCF: 𝑑 25 𝑑 2 −49 =0
2. Factor Difference of Squares: 𝑑 5𝑑+7 5𝑑−7 =0
3. Solve using Zero Product Property
𝑑=0, 𝑑=− 7 5 , 𝑑= 7 5

5. Example 4: GCF/Difference of Squares
Solve 9 𝑥 3 =4𝑥
1. Move to one side: 9 𝑥 3 −4𝑥=0
2. Factor GCF: 𝑥 9 𝑥 2 −4 =0
3. Factor Difference of Squares: 𝑥 3𝑥+2 3𝑥−2 =0
4. Solve using ZPP:
𝑥=0, 𝑥=− 2 3 , 𝑥= 2 3

6. Example 5: Repeated Factoring
B =1
4 𝑦 2 +1 (4 𝑦 2 −1)
A= 2y
B= 1
(4 𝑦 2 +1)(2𝑦−1)(2𝑦−1)

7. Example 6: Repeated Factoring
9− 𝑥 𝑥 2
(3−𝑥)(3+𝑥)(9+ 𝑥 2 )

8. Example 7: Multiple Techniques
Factor 2 𝑚 3 + 𝑚 2 −50𝑚−25
2 𝑚 3 + 𝑚 2 +(−50𝑚−25)
𝑚 2 2𝑚+1 +−25(2𝑚+1)
(2𝑚−1)( 𝑚 2 −25)
(2𝑚−1)(𝑚+5)(𝑚−5)

9. Example 8: Multiple Techniques
Factor 𝑥 4 +6 𝑥 3 −36 𝑥 2 −216𝑥
𝑥( 𝑥 3 +6 𝑥 2 −36𝑥−216)
𝑥[ 𝑥 3 +6 𝑥 2 + −36𝑥−216 ]
𝑥 𝑥 2 𝑥+6 +−36 𝑥+6
𝑥(𝑥+6)( 𝑥 2 −36)
𝑥(𝑥+6)(𝑥+6)(𝑥−6)