1 3 Algebraic Expressions Terms to know Variable

1. 3 Algebraic Expressions

Terms to know • Variable: a symbol, usually a letter, that represents one or more numbers • Algebraic Expression/Variable Expression: an expression that contains one or more variables • Evaluate: when you substitute numbers in for the variables in an expression and follow the order of operations to get an answer • Term: a number, a variable, or a product of a number and one or more variables • Coefficient: numerical factor in a term (the number in front of the variable)

What is the Order of Operations ? P – Parenthesis first E – Exponent next M Multiplication and Division D from left to right A Addition and Subtraction S from left to right = 15

Evaluating an Algebraic Expression White Boards 2. Evaluate 3 x – 4 y + x – y for x = 4 and y = – 2. = 3(4) – 4(– 2) + (4) – (– 2) = 12 – (– 8) + 4 – (– 2) = 20 + 4 – (– 2) = 26

Properties for Simplifying Algebraic Expressions Let a, b, and c represent real numbers. Definition of Subtraction a – b = a + (–b) Definition of Division a÷b= =a , b≠ 0 Distributive Property for Subtraction a(b – c) = ab – ac Multiplication by 0 0 a=0 Multiplication by -1 – 1 a = –a Opposite of a Sum –(a + b) = –a + (–b) Opposite of a Difference –(a – b) = b – a Opposite of a Product –(ab) = –a b = a (–b) Opposite of an Opposite –(–a) = a

Simplifying Algebraic Expressions “Like terms”: Terms that have the same variables raised to the same power. (+/ - coefficients, keep variables the same) = Ex. 3 Ex. 4 = =

Evaluating Algebraic Expressions Ex. 5 Simplify First = Substitute Values 4(4) – 5(-2) = 16 – (-10) = 26

White Boards 6. Evaluate 7. Evaluate for