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Slide 1

Simplifying Expressions

By: Karen Overman

Slide 2

Objective

This presentation is designed to give a brief review of simplifying algebraic expressions and evaluating algebraic expressions.

Slide 3

An algebraic expression is a collection of real numbers, variables, grouping symbols and operation symbols.

Here are some examples of algebraic expressions.

Slide 4

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.

Slide 5

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.

Slide 6

a ( b + c ) = ba + ca

To simplify some expressions we may need to use the Distributive Property

Do you remember it?

Distributive Property

Slide 7

Examples

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

Slide 8

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.

Slide 9

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.

Slide 10

Like terms are terms with the same variables raised to the same power.

- Algebraic Expressions
- Distributive Property
- Practice Problem
- Like Terms
- Combining Like Terms
- Collecting Like Terms Example
- Both Skills
- Evaluating Expressions
- Common Mistakes

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