# Simplifying Expressions Simplifying Expressions Definitions Simplify to reduce

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Simplifying Expressions

Simplifying Expressions: Definitions Simplify – to reduce into simplest form Coefficient- a number multiplied by a variable Ex: 1 x² + 3 x² Term - the parts in a expression that are to be added or subtracted. Ex: 10 x² + 4 x – 3 x Like Terms – terms with the same variables raised to the same powers. Ex: 10 x² + 4 x – 3 x

Combining Like Terms 4 x²y + 2 x²y + 3 xy² =6 x²y + 3 xy²

Commutative Property You can add numbers in any order and you can multiply numbers in any order. Example of Addition 2+7=7+2 Example of Multiplication 3 x 9=9 x 3 Algebraic rule: a+b=b+a axb=bxa

Associative Property When you are only adding or multiplying, you can group any of the numbers together Example of Addition Example of Multiplication 6+8+2 7 x 4 x 5 = (6 + 8) + 2 = (7 x 4) x 5 = 6 + (8 + 2) = 7 x (4 x 5) Algebraic rule: a + b +c = (a + b) + c = a + (b + c) Algebraic rule: a x b x c = (a x b) x c = a x (b x c)

Distributive Property You can multiply a number by the sum or you can multiply each number in the sum and then add. Example: 3(4 + 8) = 3(4) + 3(8) Algebraic rule: a(b + c) = ab + ac

Simplify the expression: 2(x + 6) + 3 x Procedure Justification 2 x + 2(6) + 3 x Distributive property 2 x + 12 + 3 x 2 x + 3 x + 12 Multiply Commutative Property (2 x + 3 x) + 12 Associative Property = 5 x + 12 Combine like terms.

On Your Own: Simplify and Justify Problem 1: 6(x – 4) + 9 Problem 2: -12 x – 5 x + 3 a + x

Order of Operations A rule for evaluating expressions. AKA PEMDAS or Please Excuse My Dear Aunt Sally First: P [(Parenthesis) (or other grouping symbols)] Second: E Exponents Third: Multiplication/division from left to right MD Fourth: AS Additions/subtraction from left to right

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