Jordyn wants to gain less than 5 pounds over the Christmas break

A. 2(3xy + 4xy - 4xy -8y) = 2(3xy - 8y)

B.  2y(3x - 8)

Step-by-step explanation:

a. Given that;

        2x3y + 8xy − 4x2y − 16y

the greatest common factor in the expression is 2, so that;

            2x3y + 8xy − 4x2y − 16y = 2(3xy + 4xy - 4xy -8y)

                                                    =  2(3xy - 8y)

Rewritting the expression, we have;

              2x3y + 8xy − 4x2y − 16y =  2(3xy - 8y)

Thus factoring out the greatest common factor, the expression becomes;

                                      2(3xy - 8y)

b. To factor the expression completely,

            2x3y + 8xy − 4x2y − 16y = 6xy + 8xy - 8xy - 16y

                                                     = 6xy -16y

                                                     = 2(3xy - 8y)

Then, the entire expression can be factorized as;

                                  2y(3x - 8)