# Algebraic Expressions Objectives: 1)To evaluate algebraic expressions 2)To simplify algebraic expressions.

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Algebraic Expressions Objectives: 1)To evaluate algebraic expressions 2)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 – b 2 + ab for a = 3 and b = -1 Replace the variables with numbers but put them in parenthesis 3(3) – (-1 2 ) + (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 a.3k – k  2k b.5z 2 – 10z – 8z 2 + z  5z 2 – 8z 2 – 10z + z  -3z 2 – 9z c.- (m + n) + 2(m – 3n)  - m – n + 2m – 6n  - m + 2m – n – 6n  m – 7n

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