Pre-Algebra Demystified

and the ‘‘x’’ is a variable. When no sign is written between a number and a
variable or between two or more variables, it means multiplication. Hence
the expression ‘‘3x’’ means ‘‘3 times x or to multiply 3 by the value of x. The
expression abc means a times b times c or abc.
The number before the variable is called thenumerical coefficient. In the
algebraic expression ‘‘3x’’, the 3 is the numerical coefficient. When the numer-
ical coefficient is 1, it is usually not written and vice versa. Hence, xy means
1xy. Likewise, 1xy is usually written as xy. Also
xy means
1xy.
An algebraic expression consists of one or moreterms.Atermis a number
or variable, or a product or a quotient of numbers and variables. Terms are
connected byþor
signs. For example, the expression 3xþ2y
6 has
3 terms. The expression 8pþ2q has two terms, and the expression 6x^2 y
consists of one term.

Evaluating Algebraic Expressions

In order to evaluate an algebraic expression, substitute the values of the
variables in the expression and simplify using the order of operations.

EXAMPLE

Evaluate 2xy when x¼2 and y¼5.

SOLUTION

2xy¼ 2 ð 2 Þð 5 Þ

¼ 20

Hence, when x¼2 and y¼5, the value of the expression 2xy is 20.

EXAMPLE

Evaluate
3x^2 when x¼
6

SOLUTION

3x^2 ¼
 3 ð
 6 Þ^2

¼
 3 ð 36 Þ

¼
 108

CHAPTER 7 Expression and Equations 127