Algebraic Expressions

Algebraic Expressions Objectives: To evaluate algebraic expressions To simplify algebraic expressions

Definitions Variable: a symbol that represents one of more numbers Algebraic Expression: AKA variable expression. An expression containing one or more variables Evaluate: substituting numbers for variables in an expression and simplifying Term: a number, variable or the product of a number and variable Coefficient: The numerical factor in a term

Properties for Simplifying Algebraic Expressions Definition of Subtraction: a – b = a + (-b) Definition of Division a ÷ b = a/b = a  1/b, b ≠ 0 Distributive Property a(b + c) = ab + ac ; a(b – c) = ab – ac Zero Product Property 0  a = 0

Properties for Simplifying Algebraic Expressions (continued) Multiplicative Inverse: -1  a = -a Opposite of a Sum: • (a + b) = -a + -b Opposite of a Difference • (a – b) = b – a

Properties for Simplifying Algebraic Expressions (continued) Opposite of a Product • -(ab) = -a b = a  -b Opposite of an Opposite • -(-a) = a

Example #1: Evaluating an Algebraic Expression Evaluate 3a – b2 + ab for a = 3 and b = -1 Replace the variables with numbers but put them in parenthesis 3(3) – (-12) + (3)(-1) 9 – (1) + (-3) 9 – 1 – 3 8 – 3 5 We’ve simplified all we can, so this is the final answer

Example #2: Combining Like Terms • 3k – k • 2k • 5z2 – 10z – 8z2 + z • 5z2 – 8z2 – 10z + z • -3z2 – 9z • - (m + n) + 2(m – 3n) • - m – n + 2m – 6n • - m + 2m – n – 6n • m – 7n

Algebraic Expressions