Rational Expressions:Multiply & Divide Polynomials

Aim: Simplify a polynomial expression by multiplying and/or dividing polynomials.

Do Now:

1. Simplify by using the distributive property: 4 (6n – 3)

2. Simplify: a3 a4

a3 + 4

4 6n

24n4 - 3

- 12

a7

Notice the difference:

( ) ( )+ 1. Drop the ( )2. Combine like terms

( ) ( )-

( ) ( )

What should be done …

1. Change to addition2. Add the polynomials

1. Distribute each term2. Combine like terms

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)

x2 – 3x + 2x - 6

x2 – x - 6x2 – 3x + 2x - 6

Let’s go CRAZY!

Simplify: (2a + 1)(a2 – 2a – 2) + 3a2

1. Parentheses ( )

2. Combine like terms

2a3 – 4a2 - 4a + a2 – 2a – 2 + 3a2

2a3

2a3 – 4a2 - 4a + a2 – 2a – 2 + 3a2

- 6a

Try theseSimplify the following:

1. 2 – 5 (-3x + 5) – 7x

2. (2x – y) (3x – 4y)

3. (2x + 3)(x2 + x – 5)

8x - 23

6x2 – 11xy + 4y2

2x3 + 5x2 – 7x - 15

Remember

When you multiply the same bases,

a3 a2

you can add the exponents.

= a3 + 2 = a5

Hence when you divide the same bases,

a3 a2

you can subtract the exponents.

= a3 - 2 = a1 = a

Divide PolynomialsSimplify:

1. Break up the numerator

2. Simplify each fraction

Try these

Simplify the following:

1. 28p3q3

7p2q3

2. 18x + 36 9

3. 10a6b8 + 8a3b5

ab

= 4p

= 2x + 4

= 10a5b7 + 8a2b4

Why is it useful to know equivalent forms?