1. R EVIEW 6.1: T HINGS TO M EMORIZE ! Naming by DegreeNaming by Number of Terms DegreeNameNumber of TermsName 0Constant1Monomial 1Linear2Binomial 2Quadratic3Trinomial 3CubicMany (4 or more)Polynomial 4Quartic 5Quintic

2. 6.2 M ULTIPLYING P OLYNOMIALS Warm Up Multiply. 1. x(x 3 ) 3. 2(5x 3 ) 5. xy(7x 2 ) 6. 3y 2 (–3y) 2. 3x 2 (x 5 ) 4. x(6x 2 ) Multiply polynomials. Use binomial expansion to expand binomial expressions that are raised to positive integer powers. Learning Goals Why Learn This? Business managers can multiply polynomials when modeling total manufacturing cost

3. Find each product. Example 1: Multiplying a Monomial and a Polynomial A. 4y 2 (y 2 + 3)B. fg(f 4 + 2f 3 g – 3f 2 g 2 + fg 3 ) Distribute and remember your exponent laws: C. 3cd 2 (4c 2 d – 6cd + 14cd 2 )

4. Find the product. Example 2A: Multiplying Polynomials (a – 3)(2 – 5a + a 2 )(y 2 – 7y + 5)(y 2 – y – 3) Find the product. y4y4 –y3–y3 –3y 2 –7y 3 7y27y2 21y 5y25y2 –5y–15 y 2 –y –3 y2y2 –7y 5 y 4 – 8y 3 + 9y 2 + 16y – 15

5. Check It Out! Example 3 Mr. Nat manages a manufacturing plant. From 1990 through 2005 the number of sunglasses produced (in thousands) can be modeled by N(x) = 0.02x 2 + 0.2x + 3. The average cost per unit (in dollars) can be modeled by C(x) = –0.004x 2 – 0.1x + 3. Write a polynomial T(x) that can be used to model the total costs.

6. Example 4: Expanding a Power of a Binomial Find the product. (a + 2b) 3

7. Do you see the pattern in Pascal’s Triangle? Continue it! What do you notice about the binomial expansion and Pascal's triangle?? Do you notice anything about the exponents of the binomial expansion??? T HE M OST B EAUTIFUL T RIANGLE : P ASCAL ’ S T RIANGLE ! M AKING L IFE S IMPLE

8. Ex5: Using Pascal’s Triangle to Expand Binomial Expressions Expand each expression. A. (k – 5) 3 B. (3x + 1) 4