Adding and Subtracting Polynomials

Combining Like Terms

In order to combine like terms, the terms must contain exactly the same variables to the same powers.

Example 1: Simplify the expression by combining like terms.

7x5 + 2x2 − 3x2 + 3 − x5

Solution:

Rewrite the expression so that like terms are grouped:

(7x5 − x5) + (2x2 − 3x2) + 3

Add the coefficients for each set of like terms. The variables carry along:

7x5 − x5 = (7− 1) x5 = 6x5

2x2 − 3x2 = (2 − 3)x2 = − 1x2 = −x2

The simplified form of 7x5 + 2x2 − 3x2 + 3 − x5 is 6x5 − x2 + 3.

Adding and Subtracting Polynomials

Be sure to change the subtraction to addition before combining like terms.

Example 2: Subtract the polynomials.

(4x − 5y2 + 2 − x2) −(−2y + 2x2 − 3x + 7)

Solution:

Change the division into addition by distributing negative one through the 2nd set of parentheses. The sign of each term in the 2nd parentheses changes.

(4x −5y2 + 2 − x2) −(−2y + 2x2 − 3x + 7)

= 4x −5y2 + 2 − x2 + 2y − 2x2 + 3x − 7

Rewrite the expression so that like terms are grouped:

(4x + 3x) + ( − x2 − 2x2) + (2 − 7) −5y2 + 2y

Combine like terms by adding the coefficients.

The simplified form of (4x − 5y2 + 2 − x2) −(−2y + 2x2 − 3x + 7) is
7x −3x2 − 5 −5y2 + 2y .

Add: (5x2+7x-4)+(3x2-6x+2)
Combine like terms: 2q3+3q2-4q-q3+5q2
Subtract: (2a2+3a-1)-(4a2+5a+6)