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

Question

I need help with this question. 

Answer 1

     2x²(x + 1)(x + 3) - 6x² 

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.

Answer 2

2x²(x+1)(x+3)-6x²

= 2x²[(x+1)(x+3)-3]

= 2x²(x²+4x)

= 2x³(x+4)