7. simplify (2x – 2y)(2y + 8) = ?

a. 4xy + 16x – 4y2 – 16y
b. 4xy – 16x – 4y2 – 16y
c. 4xy – 4y2
d. 4xy + 16x + 4y2 + 16y

4xy + 16x - 4y^2 - 16y (Answer A)

Step-by-step explanation:

Factoring 2 out of both binomials inside parentheses makes this problem a bit simpler to handle:

(2x – 2y)(2y + 8) = 2(x - y)(2)(y + 4) = 4(x - y)(y + 4)

Multiplying out the two binomial terms results in:

4 (xy + 4x - y^2 - 4y)

Performing the indicated multiplication results in:

4xy + 16x - 4y^2 - 16y.

This agrees with Answer A.  Please note, however, that y2 must be written as y^2 (the square of y) to be proper.

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