# 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.

7x^{5} + 2x^{2} − 3x^{2} + 3 − x^{5}

* Solution*:

Rewrite the expression so that like terms are grouped:

(7x^{5} − x^{5}) + (2x^{2} − 3x^{2}) + 3

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

7x^{5} − x^{5} = (7− 1) x^{5} = 6x^{5}

2x^{2} − 3x^{2} = (2 − 3)x^{2} = − 1x^{2} = −x^{2}

**The simplified form of 7x ^{5} + 2x^{2} − 3x^{2} + 3 − x^{5} is 6x^{5} − x^{2} + 3. **

# Adding and Subtracting Polynomials

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

* Example 2*: Subtract the polynomials.

(4x − 5y^{2} + 2 − x^{2}) −(−2y + 2x^{2} − 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 −5y^{2} + 2 − x^{2}) −(−2y + 2x^{2} − 3x + 7)

= 4x −5y^{2} + 2 − x^{2} + 2y − 2x^{2} + 3x − 7

Rewrite the expression so that like terms are grouped:

(4x + 3x) + ( − x^{2} − 2x^{2}) + (2 − 7) −5y^{2} + 2y

Combine like terms by adding the coefficients.

**The simplified form of (4x − 5y ^{2} + 2 − x^{2}) −(−2y + 2x^{2} − 3x + 7) is **

7x −3x^{2} − 5 −5y^{2} + 2y .

^{2}+7x-4)+(3x

^{2}-6x+2)

^{3}+3q

^{2}-4q-q

^{3}+5q

^{2}

^{2}+3a-1)-(4a

^{2}+5a+6)

0 out of 0 correct.