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 ? PEMDAS 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 3x – 4y + x – y for x = 4 and y = –2. = 3(4) – 4(–2) + (4) – (–2) = 12 – (–8) + 4 – (–2) = 20 + 4 – (–2) = 24 – (–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 Simplify First = 4(4) – 5(-2) Substitute Values = 16 – (-10) = 26

White Boards 6. Evaluate for 7. Evaluate for