By: Karen Overman
This presentation is designed to give a brief review of simplifying algebraic expressions and evaluating algebraic expressions.
An algebraic expression is a collection of real numbers, variables, grouping symbols and operation symbols.
Here are some examples of algebraic expressions.
Consider the example:
The terms of the expression are separated by addition. There are 3 terms in this example and they are .
The coefficient of a variable term is the real number factor. The first term has coefficient of 5. The second term has an unwritten coefficient of 1.
The last term , -7, is called a constant since there is no variable in the term.
Lets begin with a review of two important skills for simplifying expression, using the Distributive Property and combining like terms. Then we will use both skills in the same simplifying problem.
a ( b + c ) = ba + ca
To simplify some expressions we may need to use the Distributive Property
Do you remember it?
Example 1: 6(x + 2)
Distribute the 6.
6 (x + 2) = x(6) + 2(6)
= 6x + 12
Example 2: -4(x 3)
Distribute the 4.
-4 (x 3) = x(-4) 3(-4)
= -4x + 12
Try the Distributive Property on -7 ( x 2 ) .
Be sure to multiply each term by a 7.
-7 ( x 2 ) = x(-7) 2(-7)
= -7x + 14
Notice when a negative is distributed all the signs of the terms in the ( )s change.
Examples with 1 and 1.
Example 3: (x 2)
= 1( x 2 )
= x(1) 2(1)
= x - 2
Notice multiplying by a 1 does nothing to the expression in the ( )s.
Example 4: -(4x 3)
= -1(4x 3)
= 4x(-1) 3(-1)
= -4x + 3
Notice that multiplying by a 1 changes the signs of each term in the ( )s.
Like terms are terms with the same variables raised to the same power.