1. Warm-Up
Any questions about homework?

2. Agenda:
Factoring Sum and Difference of Cubes
Factor Relays
Homework

3. Factoring Sum and Difference of Cubes
“Patterns”
𝑎 3 + 𝑏 3 =(𝑎+𝑏)( 𝑎 2 −𝑎𝑏+ 𝑏 2 )
𝑎 3 − 𝑏 3 =(𝑎−𝑏)( 𝑎 2 +𝑎𝑏+ 𝑏 2 )
Remember signs: same-different-positive

4. 1. 𝑥
A = x b =5
2. 𝑥 3 −27
A = x b =3
𝑎 3 + 𝑏 3
𝑎 3 − 𝑏 3
(𝑥) 3 + (5) 3
(𝑥) 3 − (3) 3
(𝑎+𝑏)(𝑎 2 −𝑎𝑏+ 𝑏 2 )
(𝑎−𝑏)(𝑎 2 +𝑎𝑏+ 𝑏 2 )
(𝑥+5)(𝑥 2 −5𝑥+25)
(𝑥−3)(𝑥 2 +3𝑥+9)

5. 3. 8 𝑥
A = 2x b =7
4. 64 𝑥 4 −27𝑥
A = 4x b =3
𝑎 3 + 𝑏 3
x(64 𝑥 3 −27)
(2𝑥) 3 + (7) 3
𝑥(𝑎 3 − 𝑏 3 )
(𝑎+𝑏)(𝑎 2 −𝑎𝑏+ 𝑏 2 )
𝑥((4𝑥) 3 − )
(2𝑥+7)((2𝑥) 2 −14𝑥+49)
𝑥(𝑎−𝑏)(𝑎 2 +𝑎𝑏+ 𝑏 2 )
(2𝑥+7)(4𝑥 2 −14𝑥+49)
x (4𝑥−3)(16𝑥 2 +12𝑥+9)

6. Other Cubics by Grouping
5. 12𝑥 3 − 9𝑥 2 +4𝑥 −3
6. 2𝑥 3 + 5𝑥 2 +6𝑥+15
3𝑥 2 (4𝑥 −3)
+1(4𝑥 −3)
𝑥 2 (2𝑥+5)
+3(2𝑥+5)
(3 𝑥 2 +1)(4𝑥 −3)
( 𝑥 2 +3)(2𝑥+5)
7. 10𝑝 3 − 20𝑝 2 +6𝑛 −12
2( 5𝑝 3 − 10𝑝 2 +3𝑛 −6)
5𝑝 2 (𝑝−2)
+3(𝑝−2)
2( 5𝑝 2 +3)(𝑝−2)

7. Factor Relays Directions: Get into groups of 4
As a new questions appears you have a new spokesperson for the group
Work as a team to get the answer
Spokesperson runs up to the board and writes their answer (make sure to keep it covered
If your team gets it right, you get one point

8. 5 𝑥 2 +5𝑥 −10
5(𝑥+2)(𝑥−1)

9. 2 𝑛 3 − 𝑛 2 +2𝑛 −1
(2𝑥−1)( 𝑥 2 +1)

10. 18 𝑥 2 −2
2(3𝑥−1)(3𝑥+1)

11. 2 𝑑 2 +12𝑑 −16
2( 𝑑 2 +6𝑑−8)

12. 125 𝑥 3 −216
(5𝑥−6)(25 𝑥 2 +30𝑥+36)

13. − 𝑣 2 +2𝑣 −1
− (𝑣−1) 2

14. 𝑥 3 +64
(𝑥+4)( 𝑥 2 −4𝑥+16)

15. 5 𝑝 2 +4𝑝 −12
(5𝑥−6)(𝑥+2)

16. 𝑣 3 − 4𝑣 2 +4𝑣 −16
(𝑥−4)( 𝑥 2 +4)

17. 2 𝑎 7 −32 𝑥 3
2 𝑥 3 (𝑥+2)(𝑥−2)( 𝑥 2 +4)

18. 25 𝑥 2 −10𝑥+1
(5𝑥−1) 2

19. 𝑥 4 −10 𝑥 2 +16
( 𝑥 2 +2)( 𝑥 2 +8)

20. 6 𝑦 𝑦 2 +15𝑥
3𝑥(𝑥+1)(2𝑥+5)