1. Lesson 9.7 Factor Special Products
Essential Question: How do you factor special products?

2. Before we start… Find each product: 𝑥+1 𝑥−1 𝑥+5 𝑥−5 2𝑦+3 2𝑦−3
Compare the first term of each product to the first term of each binomial. What do you notice? Compare the last term of each product to the last term of each binomial. What do you notice? Can you write a formula for factoring 𝑎 2 − 𝑏 2 ?

3. How do you factor special products?
Recognize the pattern you have.
Use the formula.

4. Difference of Two Squares Pattern
𝑎 2 − 𝑏 2 = 𝑎+𝑏 𝑎−𝑏
Perfect Square Trinomial Pattern
𝑎 2 +2𝑎𝑏+ 𝑏 2 = 𝑎+𝑏 2
𝑎 2 −2𝑎𝑏+ 𝑏 2 = 𝑎−𝑏 2

5. Factor
𝑦 2 −16

6. Factor
16𝑎 2 −121

7. Factor
25 𝑚 2 −36

8. Factor
𝑥 2 −49 𝑦 2

9. Factor
𝑐 2 −81

10. Factor
9 𝑦 2 −64

11. Factor
𝑛 2 −12𝑛+36

12. Factor
𝑑 2 −26𝑑+169

13. Factor
9 𝑥 2 −12𝑥+4

14. Factor
4𝑠 2 +4𝑠𝑡+ 𝑡 2

15. Factor
64𝑠 2 +80𝑠𝑡+25 𝑡 2

16. Factor
ℎ 2 +4ℎ+4

17. Factor
𝑥 2 +8𝑥+16

18. Factor
8−18 𝑛 2

19. Factor
−3 𝑚 𝑛 2

20. Factor
50 𝑚 2 −72

21. Factor
−6 𝑚 2 +54

22. Factor
−3 𝑦 2 +36𝑦−108

23. Factor
2 𝑦 2 −20𝑦+50

24. Factor
3 𝑥 2 +6𝑥𝑦+3 𝑦 2

25. Factor
2 𝑥 2 +12𝑥𝑦+18 𝑦 2

26. How do you solve a polynomial equation?
Set the equation equal to 0.
Factor the polynomial.
Set each factor equal to 0.
Solve each equation.

27. Solve
𝑎 2 +6𝑎+9=0

28. Solve
𝑤 2 −14𝑤+49=0

29. Solve
4 𝑤 2 +20𝑤+25=0

30. Solve
𝑛 2 −81=0

31. Solve
𝑎 2 =225

32. Solve
𝑥 2 =144

33. Solve
𝑤 2 −16𝑤=−64

34. Solve
16𝑤 2 −72𝑤=−81

35. How do you factor special products?

36. Ticket Out the Door
Factor
𝑥 2 −121