6th Grade Math Textbook, Fundamentals

 &KDSWHU

14-5

Multiply and Divide Monomials

Objective To model multiplication and division of monomials with algebra tiles

• To apply the Laws of Exponents to multiply and divide monomials algebraically

Angela plans to print a poster in different
sizes. She expresses each of the poster’s
dimensions in the form of a monomial.
She expresses the length of the poster as 4xand the
width as 3x. What monomial can she write to express
the area of the poster?

To express the area as a monomial, first substitute 4xfor 
and 3xfor win the formula for the area of a rectangle.

Then multiply: A w 4 x(3x)

You can use algebra tiles to model the multiplication

of monomials.

Place the three xtiles that represent the

second monomial factor vertically, and

place the fourxtiles that represent the

first monomial factor horizontally.

Build a rectangle with dimensions 3x

and 4x. The area of the rectangle, 12x^2 ,

represents the product of 3xand 4x.

Remember:

Area of a Rectangle

Aw, where Aarea,

length, and wwidth

You can also multiply two or more monomials algebraically

by following these steps:

First, multiply the coefficients.

Then multiply the variables. Be sure to use the appropriate

Laws of Exponents.

4 x(3x) [(4)(3)][(x)(x)]

 12 x(1 1) Apply the Law of Exponents for Multiplication.

 12 x^2 Simplify.

So the monomial 12x^2 expresses the area of Angela’s poster.

Apply the Commutative and

Associative Properties.

Remember:

Laws of Exponents

a^1 a

am• ana(mn)

(am)namn

4 x

3 x

xxxx

x

x

x

4 x

3 x

xxxx

x

x

x

Since the rectangle contains 12x^2 tiles, the monomial 12x^2

expresses the area of the poster.