1. Lesson 9.3 Find Special Products of Polynomials
Essential Question: How do you use special product patterns to multiply binomials?

2. Before we start…
Use FOIL and see if there’s a pattern. 𝑥+2 𝑥−2 𝑥+6 𝑥−6
Use FOIL and see if there’s a pattern. 𝑥−1 2 𝑥−2 2 𝑥+3 2 𝑥+7 2

3. Special Products
There are some binomials that have special patterns when you multiply them.
Square of a Binomial Pattern
Sum and Difference Pattern

4. How do you use special product patterns to multiply binomials?
To find the square of a binomial pattern, 𝑎+𝑏 2 or 𝑎−𝑏 2 , square a, add (or subtract) twice the product of ab, and add the square of b.
The find the sum and difference pattern, 𝑎+𝑏 𝑎−𝑏 , square a and subtract the square of b.

5. Square of a Binomial Pattern
Algebra
Example
𝑎+𝑏 2 = 𝑎 2 +2𝑎𝑏+ 𝑏 2
𝑥+5 2 = 𝑥 2 +10𝑥+25
𝑎−𝑏 2 = 𝑎 2 −2𝑎𝑏+ 𝑏 2
2𝑥−3 2 =4 𝑥 2 −12𝑥+9

6. 3𝑥+4 2

7. 5𝑥−2𝑦 2

8. 𝑥+3 2

9. 2𝑥+1 2

10. 4𝑥−𝑦 2

11. 𝑥−8 2

12. Sum and Difference Pattern
Algebra
Example
𝑎+𝑏 𝑎−𝑏 = 𝑎 2 − 𝑏 2
𝑥+3 𝑥−3 = 𝑥 2 −9

13. 𝑡+5 𝑡−5

14. 3𝑥+𝑦 3𝑥−𝑦

15. 𝑥+10 𝑥−10

16. 2𝑥+1 2𝑥−1

17. 𝑟+8 𝑟−8

18. 𝑥+7𝑦 𝑥−7𝑦

19. How do you use special product patterns to multiply binomials?

20. Ticket Out the Door
𝑥−4 2