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Using Laws Of Exponents Objective: To use the laws of exponents to multiply polynomials

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Laws Of Exponents a m a n = a m+n (ab) m = a m b m (a m ) n = a mn

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Examples of how they work 1.a m a n = a m+n a 3 a 4 = (a a a)(a a a a) = a 7 a 3 a 4 = a 3 + 4 = a 7 2.(ab) 3 = (ab)(ab)(ab) = (a a a)(b b b) = a 3 b 3 3.(a 2 ) 3 = (a 2 )(a 2 )(a 2 ) = a a a a a a = a 6 4.(a 2 ) 3 = a 2 3 = a 6

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Try These 1.(2x 3 y 2 )(-5xy 3 ) 2.(a 2 b 3 ) 4 3.(-2x 3 ) 2 4.a (a 4 ) 3 a 4 1.-10x 4 y 5 solution solution 2.a 8 b 12 solution solution 3.4x 6 solution solution 4.a 17 solution solution More examplesexamples

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(2x 3 y 2 )(-5xy 3 ) (2 -5)(x 3 x)(y 2 y 3 ) (2 -5)(x 3+1 )(y 2+3 ) -10x 4 y 5 Back to Try These!

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(a 2 b 3 ) 4 (a 2 ) 4 (b 3 ) 4 (a 24 )(b 34 ) a 8 b 12 Back to Try These!

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(-2x 3 ) 2 (-2) 2 (x 3 ) 2 (-2) 2 (x 32 ) 4x 6 Back to Try These!

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a (a 4 ) 3 a 4 a (a 12 ) a 4 a 1 + 12 + 4 = a 17 Back to Try These!

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Try A Few More 1.3x 2 (4x 2 + 2x + 1) 2.x a+b (x a – b + x a+1 ) 12x 4 + 6x 3 + 3x 2 solution x 2a + x 2a + b + 1 solution End Show

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3x 2 (4x 2 + 2x + 1) (3x 2 )4x 2 + (3x 2 )2x + (3x 2 )1 12x 4 + 6x 3 + 3x 2 Try a Few More

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x a+b (x a – b + x a+1 ) (x a+b )x a – b + (x a+b ) x a+1 x a + b + a – b + x a + b + a + 1 x 2a + x 2a + b + 1 you cannot add these together they are not like terms

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Add or subtract 1. (x 2 + 4x – 1) + (5x 2 – 6x + 4) 2. (5y 2 – 9y + 1) – (7y 2 – 8y – 6) Find the product 3.(x – 6)(3x + 4) 4.(2x + 5)(3x + 4) 6x 2 – 2x.

Add or subtract 1. (x 2 + 4x – 1) + (5x 2 – 6x + 4) 2. (5y 2 – 9y + 1) – (7y 2 – 8y – 6) Find the product 3.(x – 6)(3x + 4) 4.(2x + 5)(3x + 4) 6x 2 – 2x.

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