I need help with this question.
Do to factor the expression "2x^2(x+1)(x+3)-6x^2"
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.