Question

Help please, kind of confused

Answer 1

Explanation:

Yikes. This is quite a doozy, so pay attention. We will begin by factoring by grouping. Group the first 2 terms together into a set of parenthesis, and likewise with the last 2 terms:

`(2d^4+6d^3)-(18d^2-54d)` and factor out what's common in each set of parenthesis:

`2d^3(d+3)-18d(d+3)`. Now you can what's common is the (d + 3), so factor that out now:

`(d+3)(2d^3-18d)` BUT in that second set of parenthesis, we can still find things common in both terms, so we continue to factor that set of parenthesis, carrying with us the (d + 3):

`(d+3)2d(d^2-9)` BUT that second set of parenthesis is the difference of perfect squares, so we continue factoring, carrying with us all the other stuff we have already factored:

`(d+3)2d(d+3)(d-3)`. That's completely factored, but it's not completely simplified. Notice we have 2 terms that are identical: (d + 3):

`2d(d+3)^2(d-3)` is the completely factored and simplified answer, choice 3)