Basic Mathematics for College Students

The trinomials in Example 8 can be subtracted by writing them so that like terms

are in columns.

¡

Change signs and add,

column by column.

3 x^2  4 x 6

 2 x^2  6 x 12

x^2  2 x 18

3 x^2  4 x 6

^12 x^2  6 x 122

A-12 Appendix II Polynomials

EXAMPLE (^8) Subtract: (3x (^2)  4 x6) (2x (^2)  6 x12)
StrategyWe will change the signs of the terms of 2x^2  6 x12, drop the
parentheses, and combine like terms.
WHYThis is the method for subtracting two polynomials.
Solution
Change the signs of each term of 2x^2 
6 x12 and drop the parentheses.
Combine like terms: Think: (32)x^2 x^2 ,
( 4 6)x 2 x, and ( 6 12)18.
 x^2  2 x 18
 3 x^2  4 x 6  2 x^2  6 x 12
(3x^2  4 x6)( 2 x^2  6 x 12 )
Self Check 8
Subtract:
(5y^2  4 y2) (3y^2  2 y1)
Now TryProblem 59

1. 19 y^3 2. a^3 3. 2 y 5 4. 3 b^2 b 1 5. 4 s^2 1.3s 1 6. 3 y^3
   7.4.5a 7 8. 2 y^2  6 y 3

8

9

ANSWERS TO SELF CHECKS

Fill in the blanks.

1. If two algebraic terms have exactly the same variables
   and exponents, they are called terms.


2. 3 x^3 and 3x^2 are terms.

Fill in the blanks.

3. To add two monomials, we add the and
   keep the same and exponents.


4. To subtract one monomial from another, we add the
   of the monomial that is to be subtracted.

Determine whether the monomials are like terms. If they are,

combine them.

5. 3 y,4y 6. 3 x^2 ,5x^2


6. 3 x,3y 8. 3 x^2 ,6x


7. 3 x^3 ,4x^3 ,6x^3 10.  2 y^4 , 6 y^4 ,10y^4


8.  5 x^2 ,13x^2 ,7x^2 12. 23, 12x,25x

CONCEPTS

VOCABULARY

Complete each solution.

13.

14.

Add the polynomials.

15. 4 y 5 y 16.  2 x 3 x


16. 8 t^2  4 t^2 18. 15 x^2  10 x^2


17. 3 s^2  4 s^2  7 s^2 20.  2 a^3  7 a^3  3 a^3

PRACTICE

 x^2  9 x 5

 1 2  12 x 7 x 2  1  52

 13 x^2  2 x 52  1 2

 13 x^2  2 x 52  3  1  7 x 24

13 x^2  2 x 52  12 x^2  7 x 2

 5 x^2  5 x 5

  1  5 x 2  5

 13 x^2  2  12 x 2  1  52

13 x^2  2 x 52  12 x^2  7 x 2

NOTATION

SECTION II.2 STUDY SET