BIG TIP: Post one question at a time or else your questions will be ignored.
I will do (a).
factor completely or state that the polynomial is prime.
a.) 2x^3y - 32xy
We need to remove the grestest common factor and then divide each term by the greatest common factor.
The GCF = 2xy
2xy(x^2 - 16)
(x^2 - 16) is the difference of two perfect squares and factors out to be
(x - 4)(x + 4).
Final answer: 2xy(x - 4)(x + 4)