Vocabulary... First, we need to know some vocabulary…  Expression: a mathematical phrase that is a combination of one or more variables, constants, and operation symbols (no equal sign)  Equation: a statement that says two mathematical expressions have the same, or equal, value (equal sign)

 Variable: a symbol that represents a number; letters are often used as variables  Coefficient: a number that is multiplied by a variable in an equation or expression (the number in front of the variable, or letter)

Constant: a number in an equation or expression that is NOT multiplied by a variable Term: a number or variable that makes up an expression or an equation ex: 2, 3x, 5t, x, -7, etc.

Simplifying Algebraic Expressions There are two things that you must be able to do when simplifying algebraic expressions... The first is to be able to use the distributive property. The second is to be able to combine like terms.

Distributive Property Multiply across the parentheses – each element inside the parentheses is multiplied by the element outside the parentheses.

Examples... 3x x x x + 5

Practice… SIMPLIFY EACH EXPRESSION: 1. – 4(5a – 3b) 2. 5(7 + 3x) – y – 6(3y – 7) 4. 2(x + 3) + 3(5 – 3z)

Combining Like Terms Like terms are two or more terms that have EXACTLY the same variables. 2x2x5y5y7 6y6y Can you identify 3 sets of like terms? 4 8x8x3xy4x24x2

Combining Like Terms To combine like terms, add or subtract the coefficients. DO NOT change the variable. EXAMPLE: 9x - 3y + 4x + 2y 9x - 3y + 4x + 2y 13x - 1y 13x - y

FYI… 1x is the same as x. -1x is the same as –x. You don’t have to write the one in front of any single variable!!

Practice… SIMPLIFY EACH EXPRESSION 1. 12r + 5s – 7t + 11r + 9s – 4r 2. 8x 2 – 7x + 4x 3 – 2 – 3x 2 + 9x – y – 6(3y – 7)

Applications… Randy mowed (3x 2 + 4x – 1) yards on Monday, (2x + 6) yards on Tuesday, and (2x 2 + 8) yards on Wednesday.  How many yards did Randy mow all together?

Applications… Find the perimeter of each of the shapes pictured below: 2x+7 3x-5 X-2 x+7 2x+4 4x+1