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**Simplifying Expressions**

By: Karen Overman

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

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**Algebraic Expressions**

An algebraic expression is a collection of real numbers, variables, grouping symbols and operation symbols. Here are some examples of algebraic expressions.

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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.

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Let’s 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.

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**Distributive Property**

To simplify some expressions we may need to use the Distributive Property Do you remember it? Distributive Property a ( b + c ) = ba + ca

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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

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**Practice Problem 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 Notice when a negative is distributed all the signs of the terms in the ( )’s change.

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**Examples with 1 and –1. Example 3: (x – 2) = 1( x – 2 ) = x(1) – 2(1)**

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.

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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.

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**Examples Like Terms 5x , -14x -6.7xy , 02xy The variable factors are**

identical. Unlike Terms 5x , 8y The variable factors are not identical.

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**Combining Like Terms Recall the Distributive Property**

a (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

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**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

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**Collecting Like Terms Example**

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**Both Skills This 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 + 21 Combine like terms. - x+11

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Simplifying Example

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Simplifying Example Distribute.

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Simplifying Example Distribute.

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Simplifying Example Distribute. Combine like terms.

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Simplifying Example Distribute. Combine like terms.

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**Evaluating Expressions**

Evaluate the expression 2x – 3xy +4y when x = 3 and y = -5. To find the numerical value of the expression, simply replace the variables in the expression with the appropriate number. Remember to use correct order of operations.

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**Example Evaluate 2x–3xy +4y when x = 3 and y = -5.**

Substitute in the numbers. 2(3) – 3(3)(-5) + 4(-5) Use correct order of operations. – 20 51 – 20 31

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Evaluating Example

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Evaluating Example Substitute in the numbers.

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Evaluating Example Substitute in the numbers.

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**Evaluating Example Substitute in the numbers.**

Remember correct order of operations.

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Common Mistakes Incorrect Correct

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