Question

7. Simplify (2x – 2y)(2y + 8) = ?

A. 4xy + 16x – 4y2 – 16y
B. 4xy – 16x – 4y2 – 16y
C. 4xy – 4y2
D. 4xy + 16x + 4y2 + 16y

Answer 1

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

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.

Answer 2

A.

Explanation:

Use the distributive property.

(2x − 2y)(2y + 8)

= 2x(2y + 8) − 2y(2y + 8)

= 4xy + 16x − 4y^2 − 16y