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I can not figure out how to factor 2(x+1)(x-3)^2-3(x+1)^2(x-3) can you please help me?

I have to completely factor this expression and I can not figure out where to start.

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2 Answers

In addition to the previous answer -(x+1)(x-3)(x+9):

If we will take the minus sign out from (x-3) we will get -(3-x) , then answer will be with no minus at the front:  (3-x)(x+1)(x+9) .


First you have to factor out common terms with the smallest exponents, in this case (x+1) appears with exponents 1 and 2, and (x-3) appears also with exponents 2 and 1, so we factor each of them with exponent 1

(x+1)(x-3) [ 2(x-3) - 3(x+1) ] =

(verify this by multiplying (x+1)(x-3) by [...] and using the distributive property)

= (x+1)(x-3) [ 2x-6 -3x -3 ] (applying distributive property twice inside the [ ])

= (x+1)(x-3) (-x - 9) (grouping inside of the [ ])

and that's that!

Taking the minus sign out from the last factor, you can also write the answer as

- (x+1)(x-3)(x+9) (notice the minus sign in front and make sure you understand how it was done) 

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