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Do to factor the expression "2x^2(x+1)(x+3)-6x^2"

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2 Answers

     2x2(x + 1)(x + 3) - 6x

First, use the FOIL method to multiply the two binomials in the first part of the equation:

(x + 1)(x + 3) = (x)(x) + (x)(3) + (1)(x) + (1)(3) = x2 + 3x + x + 3

                                                                       = x2 + 4x + 3 

Multiply this by 2x2:

2x2(x + 1)(x + 3) = 2x2(x2 + 4x + 3) = 2x2(x2) + 2x2(4x) + 2x2(3)

                                                      = 2x4 + 8x3 + 6x2 


Now subtract 6x2:

2x2(x + 1)(x + 3) - 6x2 = 2x2(x2 + 4x + 3) - 6x2 = 2x4 + 8x3 + 6x2 - 6x2

                                                                      = 2x4 + 8x3 

Now we factor this expression by first factoring out the greatest common factor (gcf):

    2x4 + 8x3 = 2x3(x + 4) 

And that is the answer, since it cannot be factored any further.

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