Download Expressions Test Study Guide

Expressions Review Sheet
Application of the following concepts will be assessed on the Expressions Test.
Look over your notes, classwork, homework and quiz for examples of problems
Combining Like Terms:
Like terms have the same variable raised to the same power.
We can only add or subtract like terms. We cannot add or subtract unlike terms.
Example: 5x + 3y + 6x +2y = 11x + 5y
Note: When there is subtraction in an expression, you should change it to addition
to prevent mistakes.
Example: 3x + 2y – 2x – y = 3x + 2y + (-2x) + (-y) = x + y
Distributive Property and Factoring: a(b+c) = a(b) + a(c)
We use the distributive property when we are multiplying a number by unlike terms
in parentheses
Example: 6(2x+3) = 6(2x) + 6(3) = 12x +18
Factoring: Divide out the greatest common factor
Example: 6x + 3 = 3(2x+1)
Simplifying Algebraic Expressions
Step 1: Change addition to subtraction
Step 2: Distribute
Step 3: Combine like terms.
Equivalent Expressions
Determine if expressions are equivalent by simplifying each expression to simplest
form. Two expressions are equivalent if they are the same when in simplest form.
Writing Expressions to Represent Perimeter
In order to find the perimeter when given the side lengths of the shape, add up all
of the sides. Other expressions can be made by simplifying the expression for the
sum of all of the sides or by using multiplication for sides that are added multiple
times.
Example: A rectangle has a length of x and a width of (x+3).
Expressions for the perimeter of the rectangle:
1) x+x+x+3+x+3
2) 2(x)+2(x+3)
3) 4x+6
In order to find the length of one side of a regular polygon when given the
perimeter, divide the perimeter by the number of sides of the shape.
Example: The perimeter of a triangle is 3x+9. There are 3 sides to a triangle so
divide 3x+9 by 3. One side of the triangle will equal x+3.
Translating Words to Expressions:
Break apart the words to write them as a mathematical expression.
Less than: switch the order of the numbers
Subtracted from: switch the order of the numbers