6th Grade Math Textbook, Fundamentals

 1  1  1

4 x  3

2 x

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14-6

Place the tiles for the monomial

2 x vertically and the tiles for the

polynomial 4x3 horizontally.

Build a rectangle using algebra tiles with

the dimensions 2xand 4x3. The area

of the rectangle represents the product

of 2xand 4x3.

Multiply Polynomials by Monomials

Objective To model the product of polynomials and monomials with algebra tiles

• To apply the Distributive Property to multiply a polynomial by a monomial

Robert wants to find the area of the parallelogram
at the right. It has a base of 2xcentimeters and
a height of (4x3) centimeters. What is the area
of the parallelogram?

To find the area of the parallelogram, substitute 2x
for band 4x3 for h in the formula for the area of a
parallelogram. Then multiply: Abh 2 x(4x3)

You can use algebra tiles

to model the product of a

polynomial and a monomial.

Since the rectangle contains eight x^2 tiles and six x tiles,

the area is (8x^2  6 x) cm^2.

You can also find the product of a polynomial and a monomial

algebraically by following these steps:

Apply the Distributive Property to distribute the monomial

across the terms of the polynomial.

Then multiply the coefficients and multiply the variables.

Use the appropriate Law of Exponents.

2 x(4x3)  2 x(4x)  2 x(3) Apply the Distributive Property of Multiplication

over Subtraction.

(2 • 4)(x• x) (2 • 3)x

 8 x(1 1) 6 x Apply Law of Exponents for Multiplication.

 8 x^2  6 x Simplify.

So the parallelogram has an area of (8x^2  6 x)cm^2.

Using the Associative and Commutative Properties,

group coefficients and variables.

x

x

x

2 x

4 x 3

xxx  1  1  1

x

x

x

2 x

4 x 3

xxx

Remember:

Area of a Parallelogram

Abh, where Aarea, bbase, and hheight