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Published byMercy Holland Modified over 7 years ago

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What are the different properties that can help simplify expressions? Commutative Property Commutative Associative Distributive These only work with addition and multiplication Numbers/variables can be moved around in any order. 5+7+3 = 3+7+5 9y(5) = 5(9y) 8r 2 t = 8tr 2

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Associative Property Distributive Property Numbers can be grouped differently. (5+7x)+6x = 5+(7x+6x) 3w(w) = 3(w*w) Remove parentheses by multiplying everything on the inside by the outside term.

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Examples Watch negative signs 5(4x+2) -3(4+5y) 2x(3x-8) -8y(3y-2)

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How do you simplify expressions? Distribute first to get rid of any parentheses. Combine like terms by adding or subtracting. When adding/subtracting, you can only combine like terms. If they do not have the exact same variable, they cannot be combined. Just add/subtract numbers in front, variable stays the same. When multiplying, any variable can be multiplied. Multiply the coefficients, add exponents on variables.

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Examples 2y+4x+8y 6x+2(2x+7) 4a 3 + 6a+3a 3 +8a 4(3n+9)+5n

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Examples (a+2b)3-3a 5(m-7)-3m 4(2x-1)+10(x-5) 10-2(4x-3)

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How do you multiply binomials? What is the FOIL method? Two methods: FOIL, Magic Box Order to multiply terms: First, Outer, Inner, Last Think of as double distributing.

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Examples using FOIL (x+3)(x+8) (2x+8)(4x+3) (3y-3)(2y+9) (7w-4)(w-6)

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How do you multiply using the magic box? (x+5)(2x+3) Make a box using terms that are being multiplied. x5+ 2x + 3

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Examples using Magic Box (x-5)(x+7) (2y+3)(6y-7) (4a-5)(3a+2) (7y-4)(5y-1)

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