6th Grade Math Textbook, Fundamentals

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14-4

So the area to be wallpapered is represented by the

polynomial x^2  2 x.

Notice that in using opposite tiles for x^2 x

in the problem above, you saw that the opposite

of x^2 xis x^2 x. When a number or expression

is multiplied by 1, the product is the opposite

(additive inverse) of the number or expression.

When this property is applied to an expression

within parentheses, all the terms within the

parentheses are multiplied by 1.

Subtract Polynomials

Objective To model subtraction of polynomials with algebra tiles• To subtract

polynomials algebraically

Duncan is wallpapering one wall of his child’s room. He
wants to find the area of the paper that will cover the wall.
The area of the wall, including the window, is 2x^2  3 x.
The area of the window is x^2 x. What is the area to be
wallpapered written as a polynomial in standard form?

To find the area to be wallpapered, subtract the area of the
window from the area of the wall: (2x^2  3 x) (x^2 x)

You can use algebra tiles to model the subtraction

of polynomials.

Opposite

2 x^2  3 x

x^2 x x^2  x

2 x^2 x^2  x  3 x

x^2  2 x

Model 2x^2  3 xwith algebra tiles.

Subtract (x^2 x). To subtract, add the opposite of

(x^2 x). Model x^2 x. Then replace each tile with

its opposite to model the opposite of x^2 x.

Group like tiles. Then remove the zero pairs when possible.

Write the polynomial for the resulting model.

2 x^2  3 x (x^2  x)

Remember:

Multiplicative Property of  1

(1) • a aand a• (1) a

The Opposite of a Difference

(a b)a b b a

The Opposite of a Sum

(a b)a b