Basic Mathematics for College Students

698 Chapter 8 Summary and Review

1. Write each expression without using a
   multiplication symbol or parentheses.
   a. 6 b
   b. x y z
   c.2(t)


2. a. Write the commutative property of addition
   using the variables cand d.
   b. Write the associative property of multiplication
   using the variables r, s,and t.


3. Determine whether the variable his used as a term
   or as a factor.
   a. 5 h+ 9 b. h+ 16


4. How many terms does each expression have?
   a. 3 x^2 + 2x– 5 b. –12xyz


5. Identify the coefficient of each term of the given
   expression.

a. 16 x^2 – x+ 25 b.

6. Translate the expression m– 500 into words.


7. Translate each phrase to an algebraic expression.
   a. 25 more than the height h
   b. 100 reduced by twice the cutoff score s
   c. 6 less than one-half of the time t
   d. The absolute value of the difference of 2 and the
   square ofa.


8. HARDWARE Refer to the illustration in the next
   column.
   a. Let nrepresent the length of the nail (in inches).
   Write an algebraic expression that represents the
   length of the bolt (in inches).

x

2

y

b. Let brepresent the length of the bolt (in inches).

Write an algebraic expression that represents the

length of the nail (in inches).

9. a. CLOTHES DESIGNERS The legs on a pair of
   pants are xinches long. The designer then lets
   the hem down 1 inch. Write an algebraic
   expression that represents the length of the
   altered pants legs.
   b. BUTCHERS A roast weighs ppounds. A
   butcher trimmed the roast into 8 equal-sized
   servings. Write an algebraic expression that
   represents the weight of one serving.


10. SPORTS EQUIPMENT An NBA basketball
    weighs 2 ounces more than twice the weight of a
    volleyball.
    a. Let xrepresent the weight of one of the balls.
    Write an expression for the weight of the other
    ball.

b. If the weight of the volleyball is 10 ounces, what

is the weight of the NBA basketball?

Evaluate each algebraic expression for the given values

of the variables.

11. for


12. for


13. for , , and


14. for x  19,y  17, and z 18

xy

 xz

b^2  4 ac b 10 a 3 c 5

(x7)^2 x 1

2 x^2  3 x 7 x 5

4 in.

REVIEW EXERCISES

SECTION 8.2 Simplifying Algebraic Expressions

We often use the commutative property of

multiplicationto reorder factors and the

associative property of multiplicationto

regroup factors when simplifying expressions.

DEFINITIONS AND CONCEPTS EXAMPLES

Simplify:

Simplify:  45 ba

5

9

ba 45 

5

9

bb

5  9

1

 5

9

1

b 25 b

5(3y)( 5 3)y 15 y