Warm-Up Multiplying Monomials and Binomials

Warm-Up Multiplying Monomials and Binomials

?

Lesson

Question

Lesson Goals

Multiply

and binomials.

Apply the property.

Determine products using models.

Identify special products of

.

W2K

Words to Know

Fill in this table as you work through the lesson. You may also use the glossary to help you.

the result of a multiplication of two or more terms

a number that evenly divides into another number; a polynomial that evenly divides into another polynomial

an expression involving a sum of powers in one or more variables multiplied by coefficients, where the powers must be whole numbers

the property stating that the product of a factor times a given quantity containing a sum or difference is equal to the sum or difference of the products of that factor times each term from within the quantity

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1

Warm-Up Multiplying Monomials and Binomials

Using the Distributive Property

Use the distributive property to find the product.

-4 - 5 -4 + -5

+ -4 -5

-4 + 20

Distributive property: + =

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Instruction Multiplying Monomials and Binomials

Slide

2

Multiplication Properties of Polynomials

The following multiplication properties are true for any polynomials a, b, and c:

Closure property Commutative property

The a polynomial.

of two polynomials is

=

Associative property

() = ()

property

( + ) = +

Using the Distributive Property

Multiply: 63(-5 + 3) 63 -5 + (63)(3)

+ 183

? Product of powers rule: =

4

Multiplying a Monomial by a Binomial Using Algebra Tiles

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2 - 2 =

-

3

Instruction Multiplying Monomials and Binomials

Slide

8

Multiplying Two Binomials Using Algebra Tiles

Draw the missing algebra tiles to complete the model.

2 - 1)( - 4

22 -

+

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- 3 + 2

- 3 + 2 -

2 - - 6

4

Instruction Multiplying Monomials and Binomials

Slide

10

How to Multiply a Binomial by a Binomial Using a Model

How to multiply polynomials using a model: 1. Write each factor as headers to a row or column.

2. Multiply each entry by

and column.

3. Add the terms inside the model, combining necessary.

4. Write the resulting polynomial in

when form.

Multiplying a Binomial by a Binomial Using a Table

1. Write each factor as headers to a row or column.

2. Multiply each entry by row and column.

3. Add the terms inside the model, combining like terms when necessary.

4. Write the resulting polynomial in standard form.

Multiply: -2 + 1)(3 - 5

3

-62

+1

-5

= -62 +

-5

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