Aim: How do we multiply monomials and polynomials?

Review: Simplifying polynomialsDo Now: Simplify the following expressions 1) (+ 5x – 3) – (-4 + 2x)2) (3xy + 4yz) – (4xy -5yz)3) ()() 4) ● 5) 6) x ( x+ 3)

Agenda

-Homework review-Do now review-Quick review about exponents-Multiplying monomials -Multiplying polynomials

Vocabulary

• Monomial• Polynomial

•All powerpoints will be color coded as follows: •RED means COPY (write it down!) •BLACK means READ•YELLOW means READ and REFLECT•BLUE means DO•GREEN means NEW ASSIGNMENT (might need to be written down in your planners)

Homework # 3 due 9/16

1. (3)(4)2. (4) (5)3. (4)(5)()4. (3(4 + 5y)

Check your homework # 2 answers:1. (2x2 + 2x - 4) - (x2 + 3x - 3) = x2 - x -1

2. (5) = 3 + 3p - 33. (3 + 6 – (-6 = 12- 9 4. (d2 - d + 5) - (-d2 + d + 5) = 2d2 - 2d 5. (3p2 - 2p + 3) - (p2 - 7p + 7) = 2p2 - 5p +1

Directions:– Swap papers with the person next to you.–When you are checking someone’s work:• Put a ✔ if the answer is correct.• If the answer is incorrect, underline where the

person made a mistake and then initial the work to show that you reviewed it.

Do Now: Simplify the following expressions 1) (+ 5x – 3) – (-4 + 2x)2) (3xy + 4yz) – (4xy -5yz)3) ()() 4) ● 5) 6) x ( x+ 3)

Quick review about exponents!

= 3 • 3 = 3 • 3 • 3

What does equal?

Practice!

What do they mean?

Multiplying variables• Law of Exponents

– When a multiplying the same variables, add the powers.

– Ex: ()() = =

Let’s see it with a real numbers!

Does ( = ?

Monomial times a monomialFor multiplication only:(4x3) • (3x2) 1) Multiply the constants.

(4 • 3) = 122)Multiply like variables.

(x3 • x2) = *Remember for multiplication add exponents!*

3) Put the terms next to each other! (4 • 3)(x3 • x2)

12

Let’s try together!

()(

Practice!1. ((4)2. (()3. (()4. (()5. (()6. (()

Monomial times a polynomialFor multiplying a monomial with a polynomial, use the distributive property.

(5x3)(4x + 6x2) 1) Make a rainbow with the number outside the parentheses to the first term! Distribute (multiply) the number outside the parentheses to the first term.

(5x3)(4x + 6x2) 5x3 (4x) +

(5x3)(4x + 6x2)2) Multiply the term in front of the polynomial (big bubble) with the second term.

(5x3)(4x + 6x2) = 5x3 (4x) + (5x3)(6

**NOTE** remember you can tell when the sign is negative by looking at the number before it!

5x3 (4x) + (5x3)(6

3) Now we are multiplying monomials!Remember!– Multiply the constants–Multiply the variables–Put the constants and variables together!

Let’s try together!

3x2 (2x +3)

Try on your own!

1. 9x(5x +3)2. 3x(x4 – 4)3. x( x3 + 3)4. 3x(x4 – 4y)5. x( xy3 + 3y)

Hand this in!

On a separate sheet of paper with your first and last name on it answer the following:

1. (x2 + 3x – 2) + (-x2 + 4x – 2)2. (-8x2 + 4x – 7) - (3x2 - 5x +2)3. (x3) (x2 )4. (3x2) (7 x4 – 3x )