1. Multiplying Polynomials

2. Warm-up: Multiplying Polynomials
The “5” in the term 5x is called the ? .
Simplify using the Distributive Property: 5(3 + x)
Combine like terms: 3x2 + 5x – 8x – x.
Simplify: 2a3 • 3a3

3. Activator: Multiplying Monomials
Multiply the monomials. Simplify the answers fully.

4. Ex. 1: Multiplying 2 Binomials
Multiply: (a + 8)(a – 5)
a(a – 5) + 8(a – 5)
a2 – 5a + 8a – 8•5
a2 + 3a – 40

5. Multiplying 2 Binomials: FOIL
Multiply: (2x – 3)(3x + 2)
6x2 + 4x – 9x – 6
6x2 + – 5x – 6

6. Multiply Binomials: Your Turn
Multiply: (-3x – 1)(2x – 3)
-6x2 + 9x – 2x + 3
-6x2 + 7x + 3

7. Ex. 2 Multiply a Binomial by a Trinomial
Multiply: (a + 5)(3a2 – 2a + 7)
a(3a2 – 2a + 7) + 5(3a2 – 2a + 7)
3a3 – 2a2 + 7a + 15a2 – 10a + 35
3a3 + 13a2 – 3a + 35

8. Multiplying a Binomial by a Trinomial: Your Turn
Multiply: (3x – 3)(2x2 + 5x – 1)
3x (2x2 + 5x – 1) – 3(2x2 + 5x – 1)
6x3 + 15x2 – 3x – 6x2 – 15x + 3
6x3 + 9x2 – 18x + 3

9. Ex. 3 Multiplying Three Binomials
Multiply (r + 3)(r – 2)(r + 5) two different ways using the Associative Property of Multiplication.
(r + 3)(r – 2) • (r + 5)
(r2 – 2r + 3r – 6) • (r + 5)
(r + 5) • (r2 + r – 6)
r (r2 + r – 6) + 5 (r2 + r – 6)
r3 + r2 – 6r + 5r2 + 5r – 30
r3 + 6r2 – r – 30

10. Ex. 3 Multiplying Three Binomials
Multiply (r + 3)(r – 2)(r + 5) two different ways using the Associative Property of Multiplication.
(r + 3) • (r – 2)(r + 5)
...
should be the same answer!
r3 + 6r2 – r – 30

11. Summarizing….
If you know understand the associative and commutative properties...
If you understand how to apply the distributive property...
If you know how to FOIL to multiply binomials...
Then you should be able to multiply any polynomial by any polynomial!

12. Ex. 4 Multiplying Using Special Product Patterns
a) (2y – 5) b) (5x + 2y)(5x – 2y)

13. Multiplying Using Special Product Patterns: Your Turn
c) (3q + 2r) b) (2x + y)(2x – y)

14. Application: Geography
Read Example 5 about the National Mall in Washington DC, which is in the shape of a rectangle. Summarize the problem in your own words into your notes.

15. Partner Practice: p. 132 a-h

16. Exit Slip: 3 Question Quiz
Multiply the polynomials. Simplify the solutions.
1) (4x – 3)(2x + 1)
2) (a – 2)(a2 + 3a – 4)
3) (n – 1)(n + 1)(3n – 3)

17. Homework Assignment
p. 132 #1-29 odd