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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