Simplifying ExpressionsBy: Karen Overman

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

Algebraic ExpressionsAn 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.

Distributive Propertya ( b + c ) = ba + ca

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

Do you remember it?

Distributive Property

ExamplesExample 2: -4(x 3)Distribute the 4.

-4 (x 3) = x(-4) 3(-4) = -4x + 12Example 1: 6(x + 2)Distribute the 6.

6 (x + 2) = x(6) + 2(6) = 6x + 12

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

Hint: The idea is that the variable part of the terms must be identical for them to be like terms.

ExamplesLike Terms5x , -14x

-6.7xy , 02xy

The variable factors areidentical.Unlike Terms5x , 8y

The variable factors are not identical.

Combining Like TermsRecall the Distributive Propertya (b + c) = b(a) +c(a)To see how like terms are combined use the Distributive Property in reverse.5x + 7x = x (5 + 7) = x (12) = 12x

Example All that work is not necessary every time.Simply identify the like terms and add their coefficients.

4x + 7y x + 5y = 4x x + 7y +5y = 3x + 12y

Collecting Like Terms Example

Both SkillsThis example requires both the Distributive Property and combining like terms.5(x 2) 3(2x 7)Distribute the 5 and the 3.x(5) - 2(5) + 2x(-3) - 7(-3) 5x 10 6x + 21Combine like terms.- x+11

Simplifying Example

Simplifying Example

Distribute.

Simplifying Example

Distribute.

Simplifying Example

Distribute.

Combine like terms.

Simplifying Example

Distribute.

Combine like terms.

Evaluating ExpressionsRemember to use correct order of operations.Evaluate the expression 2x 3xy +4y whenx = 3 and y = -5.

To find the numerical value of the expression, simply replace the variables in the expression with the appropriate number.

ExampleEvaluate 2x3xy +4y when x = 3 and y = -5.Substitute in the numbers.2(3) 3(3)(-5) + 4(-5)Use correct order of operations.6 + 45 20 51 2031

Evaluating Example

Evaluating Example

Substitute in the numbers.

Evaluating Example

Substitute in the numbers.

Evaluating ExampleRemember correct order of operations.Substitute in the numbers.

Common MistakesIncorrect

Correct