Question

An expression is shown below: 2x^3y + 8xy − 4x^2y − 16y Part A: Rewrite the expression so that the GCF is factored completely. (4 points) Part B: Rewrite the expression completely factored. Show the steps of your work. (6 points)

Answer 1

2x³y + 8xy − 4x²y − 16y =
2y(x³+4x-2x²-8)  ← GCF is factored completely
2y(x(x²+4)-2(x²+4))
2y(x-2)(x²+4)  ← completely factored

Answer 2

In that polynomial, the only thing common between all the terms is a single y and the number 2.  Factoring out a 2y gives you this: 2y(x^3 + 4x - 2x^2 -8)Factoring it completely is a whole 'nother story.  You need to accomplish this by grouping like this: 2y(x^3 + 4x) - (2x^2 - 8).  What you can factor out of those sets of parenthesis that is common is simply an x, but it makes all the difference in the world cuz this is what is left after you do that:
(2y)x(x^2 + 4) - 2(x^2 + 4).  Now you have a common factor of (x^2 + 4) that can be factored out to give you this: (x^2 + 4)(2xy - 2). You can factor a 2 out of the second set of parenthesis to get (x^2 + 4) * 2(xy - 1). Rewrite it with the 2 out front to finish: 2(x^2 + 4)(xy - 1)