1. Rational Expressions: Multiply & Divide Polynomials Aim: Simplify a polynomial expression by multiplying and/or dividing polynomials.

2. Do Now: 1.Simplify by using the distributive property: 4 (6n – 3) 2.Simplify: a 3  a 4 a 3 + 4 46n6n 24n 4 - 3 - 12 a7a7

3. Notice the difference: ( ) + 1.Drop the ( ) 2.Combine like terms ( ) -  1.Change to addition 2.Add the polynomials 1.Distribute each term 2.Combine like terms

4. Multiply Polynomials Find the product of (x + 2) and (x - 3) 1. Translate 2.Parentheses ( ) F O I L 3.Combine like terms (x + 2)(x – 3) x 2 – 3x + 2x - 6 x 2 – x - 6 x 2 – 3x + 2x - 6

5. Let’s go CRAZY! Simplify: (2a + 1)(a 2 – 2a – 2) + 3a 2 1. Parentheses ( ) 2.Combine like terms 2a 3 – 4a 2 - 4a + a 2 – 2a – 2 + 3a 2 2a32a3 - 6a

6. Try these Simplify the following: 1. 2 – 5 (-3x + 5) – 7x 2. (2x – y) (3x – 4y) 3. (2x + 3)(x 2 + x – 5) 8x - 23 6x 2 – 11xy + 4y 2 2x 3 + 5x 2 – 7x - 15

7. Remember When you multiply the same bases, a3  a2a3  a2 you can add the exponents. = a 3 + 2 = a 5 Hence when you divide the same bases, a3a2a3a2 you can subtract the exponents. = a 3 - 2 = a 1 = a

8. Divide Polynomials Simplify: 1.Break up the numerator 2. Simplify each fraction

9. Try these Simplify the following: 1. 28p 3 q 3 7p 2 q 3 2.18x + 36 9 3.10a 6 b 8 + 8a 3 b 5 ab = 4p = 2x + 4 = 10a 5 b 7 + 8a 2 b 4

10. Why is it useful to know equivalent forms?