Basic Mathematics for College Students

Add polynomials.

Recall that like terms have exactly the same variables and the same exponents. For
example, the monomials

3 z^2 and  2 z^2 are like terms Both have the same variable (z) with the same

exponent (2).

However, the monomials

7 b^2 and 8a^2 are not like terms They have different variables.
32 p^2 and 25p^3 are not like terms The exponents of pare different.
Also recall that we use the distributive property in reverse to simplify a sum or
difference of like terms. We combine like termsby adding their coefficients and
keeping the same variables and exponents. For example,

and

These examples suggest the following rule.

Adding Polynomials

To add polynomials, combine their like terms.

 7 y  4 x^2

2 y 5 y 12  52 y  3 x^2  7 x^2  1  3  72 x^2

1

Appendix II Polynomials A-9

EXAMPLE (^1) Add: 5x (^3)  7 x 3
StrategyWe will use the distributive property in reverse and add the coefficients
of the terms.
WHY 5 x^3 and 7x^3 are like terms and therefore can be added.
Solution
5 x^3  7 x^3  12 x^3 Think: (57)x^3  12 x^3.
Self Check 1
Add: 7y^3  12 y^3
Now TryProblems 15 and 19
EXAMPLE 2
Add:
StrategyWe will use the distributive property in reverse and add the coefficients
of the terms.
WHY , , and are like terms and therefore can be added.
Solution
Since the three monomials are like terms, we add the coefficients and keep the
variables and exponents.
To add the fractions, add the numerators
 (^) and keep the denominator: 3  5  7 15.

15

2

t^2

3

2

t^2 

5

2

t^2 

7

2

t^2 a

3

2



5

2



7

2

bt^2

7

2 t

5 2

2 t

3 2

2 t

2

3

2

t^2 

5

2

t^2 

7

2

t^2

Self Check 2

Add:

a^3  a^3  a^3

Now TryProblem 21

5

9

2

9

1

9

EXAMPLE (^3) Add: 2x3 and 7x 1
StrategyWe will reorder and regroup to get the like terms together. Then we will
combine like terms.
WHYTo add polynomials means to combine their like terms.
To add two polynomials, we write a sign between them and combine like terms.
Self Check 3
Add:
5 y2 and  3 y 7
Now TryProblem 27