Question

12d^3+12d^2-8d-8 Factor by Grouping, show work please

Answer 1

I see that 12 shows up in 2 terms and 8 shows up in a different 2 terms.  This is a pretty good bet for factoring by grouping.

12d^3+12d^2-8d-8 = 12(d^2)(d+1) - 8(d+1)

d+1 is common to both terms of this expression?  Also note that 12 = 3*4 and 8 = 2*4, so 4 is another factor common to both terms.

Thus we have (4)(d+1) [ 3d^2 - 2]