ALGEBRAIC EXPRESSIONS
An algebraic expression is made up of the
signs and symbols of algebra. These
symbols include the Arabic numerals,
literal numbers, the signs of operation,
and so forth. Such an expression
represents one number or one quantity.
Evaluate the following algebraic
expressions when a = 4, b = 2, c = 3, x = 7,
and y = 5. Remember, the order of
operation is multiplication, division,
addition, and subtraction.
Answers:
1.53
2. 29
3. 19
4. 53
TERMS AND COEFFICIENTS
An expression containing only one term,
such as 3ab, is called a monomial (mono
means one). A binomial contains two
terms; for example, 2r + by. A trinomial
consists of three terms. Any expression
containing two or more terms may also be
called by the general name, polynomial
(poly means many). Usually special names
are not given to polynomials of more than
three times. The expression x3  3x
2
+ 7x
+ 1 is a polynomial of four terms. The
trinomial x
2
+ 2x + 1 is an example of a
polynomial which has a special name.
Identify each of the following
expressions as a monomial, binomial,
trinomial, or polynomial. (Some
expressions may have two names.)
Answers:
1. Monomial
2. Trinomial (also polynomial)
3. Monomial
4. Polynomial
5. Binomial (also polynomial)
6. Binomial (also polynomial)
COMBINING TERMS
Like terms are added or subtracted by
adding or subtracting the numerical
coefficients and placing the result in
front of the literal factor, as in the
following examples:
7x
2
 5x
2
= (7  5)x
2
= 2x
2
5b
2
x  3ay
2
 8b
2
x + 10ay
2
= 3b
2
x + 7ay
2
Combine like terms in the following
expression:
Answers:
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View Full DocumentSYMBOLS OF GROUPING
The following example shows how the rule
for removal of parentheses is applied to
algebraic expressions:
2a  (4x + 3by) = 2a + 4x  3by
Parenthesis preceded by a plus sign can
be removed without any other changes, m
the following example shows:
2b + (a b)=2b+aba+b
Enclosing Terms in Parentheses
When it is desired to enclose a group of
terms in parentheses, the group of terms
remains unchanged if the sign preceding
the parentheses is positive. This is
illustrated as follows:
Note that this agrees with the rule for
removing parentheses preceded by a plus
sign.
If terms are enclosed within parentheses
preceded by a minus sign, the signs of all
the terms enclosed must be changed as in
the following example:
In problems 1 .through 4, remove the
symbols of grouping and combine like
terms. In problems 5 through 8, enclose
the first two terms in parentheses
preceded by a plus sign (understood) and
the last two in parentheses preceded by a
minus sign.
EXPONENTS AND RADICALS
Thus the general form can be expressed
as follows:
n
a
.
n
b
= n
a+b
The algebraic rules for radicals also
remain the same as those of arithmetic.
In arithmetic,
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 Spring '11
 Espisito
 Quadratic equation, Elementary algebra

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