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# Subtraction of Polynomials Help

based on 3 ratings
By McGraw-Hill Professional
Updated on Sep 26, 2011

## Subtraction of Polynomials

You learned that whenever you subtract integers in algebra, you add the opposite. For example, –10 – (–6) = –10 + 6 = –4. To find the opposite of an integer (except 0), we change its sign. To find the opposite of a monomial, change the sign of the numerical coefficient: e.g., the opposite of –7xy is 7xy and the opposite of 8x 2 is –8x 2 .

To find the opposite of a polynomial, change the signs of every term of the polynomial: e.g., the opposite of 6x 2 – 3x + 2 is – (6x 2 – 3x +2) or –6x 2 + 3x – 2.

To subtract two polynomials, add the opposite of the polynomial being subtracted .

#### Example 1

Subtract (9x 2 + 3x – 2) – (6x 2 + 5x – 8).

#### Example 2

Subtract (2a – 3b – c) – (5a – 6b – c).

### Subtraction of Polynomials Practice Problems

#### Practice

Subtract:

1. (6x – 3) – (x + 8)

2. (2x 2 + 5x -3) - (4x 2 + 5x + 5)

3. (3a - 2b + 6) - (-5a - 3b + 4)

4. (13r - 2s) - (15s + 3r)

5. (y 2 + 6y - 10) - (-5 + 8y - y 2 )

1. 5x - 11

2. - 2x 2 - 8

3. 8a + b + 2

4. 10r - 17s

5. 2y 2 - 2y - 15

Practice problems for these concepts can be found at: Operations with Monomials and Polynomials Practice Test.

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