Simplifying Expressions By: Karen Overman

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

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.

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.

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

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

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 + 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) 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.

Examples Like Terms 5x , -14x -6.7xy , 02xy The variable factors are identical. Unlike Terms 5x , 8y The variable factors are not identical.

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

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 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

Simplifying Example

Simplifying Example Distribute.

Simplifying Example Distribute.

Simplifying Example Distribute. Combine like terms.

Simplifying Example Distribute. Combine like terms.

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.

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. 6 + 45 – 20 51 – 20 31

Evaluating Example

Evaluating Example Substitute in the numbers.

Evaluating Example Substitute in the numbers.

Evaluating Example Substitute in the numbers. Remember correct order of operations.

Common Mistakes Incorrect Correct