Simplifying Expressions Simplifying Expressions Definitions Simplify to reduce

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Simplifying Expressions

Simplifying Expressions

Simplifying Expressions: Definitions Simplify – to reduce into simplest form Coefficient- a number multiplied

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 +

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

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

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

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 +

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

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

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