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Factoring Using the Distributive Property. What. You'll Learn. To use the distributive property to factor Polynomials. Distributive Property. Remember the distributive property allows us to multiply a monomial with a polynomial. 6a(3a -7b) = 18a 2 – 42ab.

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## Factoring Using the Distributive Property

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**Factoring Using the Distributive Property**What You'll Learn To use the distributive property to factor Polynomials**Distributive Property**Remember the distributive property allows us to multiply a monomial with a polynomial 6a(3a -7b) = 18a2 – 42ab We are going to learn how to undo the distributive process, this is known as factoring (expressing the polynomial as a product of a monomial and a polynomial) Think of going from the answer back to the problem.**Let’s work a few of these.**1.) (x+2) (x+8) 2.) (x+5) (x-7) 3.) (2x+4) (2x-3)**Check your answers.**1.) (x+2) (x+8) = X2+10x+16 2.) (x+5) (x-7) = X2-2x-35 3.) (2x+4) (2x-3) = 4x2+2x-12**By learning to use the distributive property, you will be**able to multiply any type of polynomials. Example:(x+1)(x2+2x+3) (x+1)(x2+2x+3) = X3+2x2+3x+x2+2x+3**Factoring**12mn2 – 18m2n2 First find the greatest number that will divide evenly into 12 and 18 This will be 6 Next find the greatest number of variables common to both terms m and n2 Next divide 6mn2 into each term, You get 2 – 3m. This goes in the parenthesis 6 mn2 (2 – 3m) Check by multiplying back through 6mn2(2 – 3m) = 12mn2 - 18m2n2 We factored it correctly**Factor**First find the greatest number that will divide evenly into 21 and 14 21x2 – 14x3 Next find the greatest number of variables common to both terms Next divide 7x2 into each term 7 x2 (3 – 2x) Check by multiplying back through 7x2(3 – 2x) = - 14x3 21x2 Factored Correctly**(2 m + 3n – 4mn)**2 Factor Try this on your own. 4m + 6n – 8mn How did you do? Got it wrong Click here to return to instruction Got it right Click here to bring on the next problem**Factor**Try this on your own. 12p3q2 – 18p2q2 + 30pq2 6pq2(2p2 – 3p + 5) How did you do? Got it wrong Click here to return to instruction Got it right Click here to bring on the next problem

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