1. 3-2 Multiplying polynomials
Chapter 3
3-2 Multiplying polynomials

2. Problem of the day If 𝑖= −1 , then (5-3i)(4+2i)= A)14-2i B)16 C)24
D)26-2i
E)28

3. Solution to the problem of the day
The right answer is :D

4. objectives Multiply polynomials.
Use binomial expansion to expand binomial expressions that are raised to positive integer powers.

5. Multiply polynomials
To multiply a polynomial by a monomial, use the Distributive Property and the Properties of Exponents.

6. Example#1 Find each product. A. 4y2(y2 + 3)
B. fg(f4 + 2f3g – 3f2g2 + fg3)

7. Multiply polynomials
To multiply any two polynomials, use the Distributive Property and multiply each term in the second polynomial by each term in the first.

8. Example#2 Find the product. (a – 3)(2 – 5a + a2)
Method multiply horizontally

9. Example#3 5 Find the product. y2 – 7y + 5)(y2 – y – 3) The box method

10. Student guided practice
Do problems 1-6 from your book page 162

11. Application
Mr. Silva manages a manufacturing plant. From 1990 through 2005 the number of units produced (in thousands) can be modeled by N(x) = 0.02x x The average cost per unit (in dollars) can be modeled by C(x) = –0.004x2 – 0.1x Write a polynomial T(x) that can be used to model the total costs.
Total cost is the product of the number of units and the cost per unit.
T(x) = N(x)  C(x)

12. Binomial Expansion
Find the product.
(2x – 1)3

13. Pascal triangle
Notice the coefficients of the variables in the final product of (a + b)3. these coefficients are the numbers from the third row of Pascal's triangle.

14. Pascal Triangle
Each row of Pascal’s triangle gives the coefficients of the corresponding binomial expansion. The pattern in the table can be extended to apply to the expansion of any binomial of the form (a + b)n, where n is a whole number.

15. Binomial Expansion

16. Using Pascal’s Triangle to Expand Binomial Expressions
Example
Using Pascal’s Triangle to Expand Binomial Expressions
A. (k – 5)3
B. (6m – 8)3

17. Example
a. (x + 2)3
b. (x – 4)5

18. Student Guided practice
Do problems in your book page 162

19. Homework
Do problems ,27,31-33 from your book page 162

20. Closure
Today we learned how to multiply polynomials using the horizontal method and the box method. We also learned about Pascal triangle.
Next class we are going to learned how to divide polynomials