Basic Mathematics for College Students

Chapter 8 Summary and Review 697

Variables and/or numbers can be combined
with the operations of addition, subtraction,
multiplication, and division to create algebraic
expressions.

We often refer to algebraic expressionsas
simply expressions.

Expressions:

8 a(b3)

12 x

5

5 y 7

A termis a product or quotient of numbers
and/or variables. A single number or variable
is also a term. A term such as 4, that consists of
a single number, is called a constant term.

Terms: 4, y,6r,–w^3 , 3.7x^5 , –15ab^2

3

n

,

Addition symbols separate expressions into
parts called terms.

The numerical factor of a term is called the
coefficientof the term.

Since can be written as , it has three

terms.

6 a^2 a 5 6 a^2 a(5)

It is important to be able to distinguish
between the terms of an expressionand the
factors of a term.

x+ 6 6 x

xis a term. xis a factor.

 

Key wordsand key phrasescan be translated
into algebraic expressions.

5 more than can be expressed as.

25 less than twice can be expressed as.

One-half of the cost ccan be expressed as.

1

2

c

y 2 y 25

x x 5

Toevaluate algebraic expressions,we
substitute the values of its variables and apply
the rules for the order of operations.

Evaluate for and.

Substitute 2 for xand 3 fory.

In the numerator, evaluate the exponential

expressions. In the denominator, add.

In the numerator, subtract.

 5 Do the division.



 5

 1



4  9

 1

x^2  y^2

x y



22 ( 3 )^2

2 ( 3 )

x 2 y 3

x^2 y^2

xy

Term Coefficient

6

a 1

 5  5

6 a^2