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 .
0 out of 0 correct.