MATH 60
UNIT 2.4
1
ADDITION AND SUBTRACTION OF POLYNOMIALS (B. Shakib 11/88)
The most important point to keep in mind in adding and subtracting polynomials is to be able to distinguish
between like and unlike terms. So before doing any examples, let us explain what we mean by like/unlike
terms.
Consider the two terms:
a 2 and a 3
These terms are unlike because, as noticed, they do not even ‘look’ the same. For two terms to be alike ,
every variable (not coefficient) must be the same; thus the two terms 3a² and -2a² are like terms (we do not
consider the coefficients -2 and 3). Now in addition and subtraction of polynomials either operation must
be done only between the like terms (that is no operation taking place between unlike terms).
Example 1:
Simplify
3a 2  7a 2
a)
First thing to do is to see whether or not two terms are common. In this case the two
terms are “like terms” (both are a²).
b) Next thing to do is to add (or subtract) the coefficients. In this case, that would be
3  7  4
So the answer will be:
3a2  7a2  4a2
Example 2:
Simplify the following expressions.
a)
5a  2a 2
b)
3a3  5a3  (3  5)a3  2a3
c) 2a2  3a  4a 2  7a
the two terms cannot be added because they are “unlike terms.”
do subtraction on coefficients only
try to group “like terms” together (do the same thing for
“unlike terms”).
(2a 2  4a 2 )  (3a  7a)
2a 2  10a
I cannot simplify this expression any further because they are
“unlike terms.”
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MATH 60
UNIT 2.4
2
With previous instructions kept in mind, simplify the following expressions:
1.
2a 4  5a 2  2
2.
xy3  x3 y  xy3
3.
8b2  8a 2  8ab2
4.
2a2  3ab2  3a2  3ab2
5.
6 x  7 y  3x 2  8 y  4 x 2  5x
6.
3a 2b  4ba 2
7.
x 2  2 x  x3  2 x 2  5 x
8.
8 y 2  2 x2  4 xy 2  4 x 2 y 2
9. 12ab
2
 5a2b  6ab2
10.
7 xy3  5x3 y3  5xy3  15x3 y3
Answers
1.
Cannot be simplified any further
{think about why it cannot be simplified}
2.
2xy3  x3 y
3.
Cannot be simplified and further
4.
a 2
5.
 x  15 y  x 2
6.
 a 2b
7.
x 3  x 2  3x
8.
cannot be simplified any further
9.
5a 2b  6ab2
10.
12 xy3  20 x3 y3
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No part of this work may be reproduced without the prior written consent of the Cerritos College Math Learning Center.