Basic Mathematics for College Students

Appendix II Polynomials A-19

Solution

a.Multiply:

Multiply by 5.

Multiply by.

In each column, combine like terms.

b.With this method, it is often necessary to leave a space for a missing term to
vertically align like terms.
Multiply:

Multiply by.

Multiply by.

Leave a space for any missing powers of.

In each column, combine like terms.

y

6 y^3  5 y 4  4 y^2

6 y^3  5 y 4  3

6 y^3  5 y 4

  4 y^2  3

 18 y^3  15 y 12

 24 y^5  20 y^3  16 y^2

 24 y^5  2 y^3  16 y^2  15 y 12

3 a^2  4 a 7 2 a

3 a^2  4 a 7

3 a^2  4 a 7

 2 a 5

15 a^2  20 a 35

6 a^3  8 a^2  14 a

6 a^3  7 a^2  6 a 35

Fill in the blanks.

1. is the product of two.


2. is the product of two.


3. In the acronym FOIL, F stands for terms, O for
   terms, I for terms, and L for terms.


4. is the product of a
   and a.

Fill in the blanks.

5. To multiply two polynomials, multiply term of
   one polynomial by term of the other
   polynomial, and then combine like terms.


6. Label each arrow using one of the letters F, O, I, or L.
   Then fill in the blanks.

First Outer Inner Last

(2x5)(3x4)   

CONCEPTS

(2a4)(3a^2  5 a1)^

(2a4)(3a5)^

(2x^3 )(3x^4 )^

VOCABULARY 7. Simplify each polynomial by combining like terms.

a.

b.

8. a. Add:
   b. Subtract:
   c. Multiply:

Complete each solution.

9.

10.

11.

12. 3 x^2  4 x 2
    2 x 3
     12 x 6
    6 x^3  8 x^2  4 x
     17 x^2   6

 6 x^2   10

 6 x^2    10

(2x5)(3x2) 2 x(3x) (2) (3x) (2)

  14 x^2  35 x

7 x(3x^2  2 x5) (3x^2 ) (2x) (5)

(9n^3 )(8n^2 )(9 )( n^2 )

NOTATION

(x4)(x8)

(x4)(x8)

(x4)(x8)

5 x^4  3 ax^2  5 ax^2  3 a^2

6 x^2  8 x 9 x 12

SECTION II.3 STUDY SET

1. 14 a^8 2. a. 15 y^4  12 y^2 b. 15 x^3  10 x^2  15 x 3. a.y^2  4 y 3 b. 6 a^2 a 2

4. 25 x^2  40 x 16 5. 6 a^6  5 a^4  3 a^3 a^2 a 6. a. 6 x^3  8 x^2  7 x 10
   b. 4 x^4  8 x^3  8 x^2  12 x 3

ANSWERS TO SELF CHECKS