Simplifying Expressions August 15, 2013

Evaluating Example/ Warm-up

Evaluating Example Substitute in the numbers.

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

Objective Students will be able to simplify algebraic expressions by applying the distribution property and combining like terms.

Objective By the end of class, students will be able to simplify: And be able to answer the question: what two math skills must I master to simplify 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.

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

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) = 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.

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 Distribute. Combine like terms.

Simplifying Example Can you answer this?? Distribute. Combine like terms.

Common Mistakes IncorrectCorrect

Objective Students will be able to simplify algebraic expressions by applying the distribution property and combining like terms. What two math skills must I master to simplify algebraic expressions?