Simplifying Variable Expressions with Like Terms

1. Simplifying Variable Expressions Like Terms: All terms with same variable part. (same letters have same exponents). Procedure: Simplifying variable expressions with like terms. If two terms are like, “combine” the like terms by adding the numerical coefficients (the variable part of the terms remain unchanged) Example 1. Simplify the following: Answers: * Note: terms are usually left in alphabetical order. If the terms have exponents with the same variable, then the order is from highest exponent to lowest exponent. This is called descending order. * Your Turn Problem #1 Simplify the following: Answers:

2. Simplifying variable expressions involving multiplication of a numerical and a variable factor. Procedure: When multiplying a numerical factor and a variable factor: Step 1: Multiply the numerical factor times the numerical coefficients. Step 2: Attach the variable. Example 2. Simplify the following: Answers: Note: we are actually using the associative property: a (b  c) = (a b) c. 5(7x) = (57) x Your Turn Problem #2 Simplify the following: Answers:

3. Simplifying a variable expression using the Distributive Property. Distributive Property: a (b +c) = ab +ac. Procedure: If given a factor located in front of a set of parentheses with unlike terms within the parentheses: Step 1. Multiply each term inside parentheses by the factor located outside the parentheses. Step 2. Rewrite the problem without parentheses. Note: If you are directed to simplify an expression with only a minus in front, change it to “1” and then distribute. Example 3. Simplify the following: Answers: Your Turn Problem #3 Simplify the following: Answers:

4. Simplifying general variable expressions Procedure: In simplifying expressions involving parentheses: Step 1: Use the distributive property to eliminate parentheses. Step 2: Combine like terms. Example 4. Simplify the following: Answers: Your Turn Problem #4 Simplify the following: Answers:

5. To evaluate a variable expression. Evaluating a variable expression. When values are given for the variables in a problem, then the variable expressions can be evaluated. Procedure: To evaluate a variable expression: Step 1. Replace each variable with the number given for each. If the variable is given to be a negative value, or if variable is to be multiplied or divided, place the given value within a set of parentheses. Step 2. Simplify expressions by using Order of Operations Agreement (PEMDAS) Example 5.Evaluate the algebraic expressions for the given values of the variables. Answers: Your Turn Problem #5 Evaluate the algebraic expressions for the given values of the variables. Answers:

6. Some problems may be expressed in a written form as opposed to using mathematical or algebraic symbols. The following are some phrases that are associated with specific operations. Addition (symbol: + )Subtraction (symbol:  ) added to minus more than less than (reverse order of variables) the sum of less increased by the difference of the total of take away decreased by Multiplication (symbol:  )Division (symbol: write as fraction) times divided by of the quotient of the product of the ratio of multiplied by Exponent (power) 2nd power: the square of 3rd power: the cube of to the nth power

7. Translating verbal expressions to mathematical (variable) expressions Procedure: To translate verbal expressions to variable expressions: Step 1: Identify words and phrases that indicate mathematical operations. Step 2: Without changing order of verbal expression, translate to a variable expression. (Note: The only time you reverse the order of the expression is when the words "subtracted from" or "less than" are used). Example 6. Translate the following into an algebraic expression. Your Turn Problem #6 Answers: Translate the following into an algebraic expression. The End. B.R. 5-7-07