2. To multiply a polynomial by a monomial Multiply the numbers together Multiply the same letters together by adding the exponents Ex – 3x 3 y 6 z 8 ( 5x 9 y 4 z 7 )= 16 a 9 b 3 (5a 7 z)= 15x 12 y 10 z 15 80a 16 b 3 z

3. use the Distributive Property and the Properties of Exponents. To multiply a polynomial by a monomial

4. Find each product. Multiplying a Monomial and a Polynomial A. 4y 2 (y 2 + 3) Distribute. B. fg(f 4 + 2f 3 g – 3f 2 g 2 + fg 3 ) (4y 2  y 2) + (4y 2  3) Multiply. 4y 4 + 12y 2 Distribute. Multiply. (fg  f 4) + (fg  2f 3 g) – (fg  3f 2 g 2) + (fg  fg 3) f 5 g + 2f 4 g 2 – 3f 3 g 3 + f 2 g 4

5. Find each product. a. 3cd 2 (4c 2 d – 6cd + 14cd 2 ) Distribute. b. x 2 y(6y 3 + y 2 – 28y + 30) (3cd 2  4c 2 d) – (3cd 2  6cd) + (3cd 2  14cd 2) Multiply. 12c 3 d 3 – 18c 2 d 3 + 42c 2 d 4 Distribute. Multiply. (x 2 y  6y 3) + (x 2 y  y 2) – (x 2 y  28y) + (x 2 y  30) 6x 2 y 4 + x 2 y 3 – 28x 2 y 2 + 30x 2 y

6. Quotient of exponents – subtract the exponents an =an = Examples a n-m amam Bases must be the same a 5 = a 3 a 5-3 = a 2 p 5 = p 9 p 5-9 = p -4

7. Power to a Power – multiply the exponents (a) n m = a nm Examples (5 2 ) 3 5656 (3 3 a 5 ) 4 3 12 a 20 = 531441a 20 (2 2 s 5 t 7 x 3 ) 5 2 10 s 25 t 35 x 15 = 1024s 25 t 35 x 15

8. Monomial to a power – distribute the exponent (ab) n = a n b n Examples (5x) 3 5 3 x 3 = 125x 3 (ab) 4 a4b4a4b4 (2stx) 5 2 5 s 5 t 5 x 5 = 32s 5 t 5 x 5

10. Simplify the expression. Assume all variables are nonzero. Example 3B: Using Properties of Exponents to Simplify Expressions Quotient of Powers Negative of Exponent Property Power of a Product (yz 3 – 5 ) 3 = (yz –2 ) 3 y 3 (z –2 ) 3 y 3 z (–2)(3)

11. Check It Out! Example 3a Simplify the expression. Assume all variables are nonzero. Power of a Power Power of a Product (5x 6 ) 3 53(x6)353(x6)3 125x (6)(3) 125x 18

12. Page 355 # 1-28 omit 10 & 11