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Simplifying Expressions

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: 10x² + 4x – 3x

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Simplifying Expressions

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  1. Simplifying Expressions

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

  3. CombiningLike Terms • 4x²y + 2x²y + 3xy² • =6x²y + 3xy²

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

  5. 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: Algebraic rule: • a + b +c = (a + b) + c = a + (b + c) a x b x c = (a x b) x c = a x (b x c)

  6. 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

  7. Simplify the expression:2(x + 6) + 3x

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

  9. Order of Operations • A rule for evaluating expressions. • AKA PEMDAS or Please Excuse My Dear Aunt Sally

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