Let's simplify the expression step by step:
We start with the expression [tex]\((2x - 2y)(2y + 8)\)[/tex]. To simplify this, we apply the distributive property (also known as the FOIL method for binomials), which involves multiplying each term in the first binomial by each term in the second binomial.
First, we distribute [tex]\(2x\)[/tex] from [tex]\((2x - 2y)\)[/tex]:
[tex]\[ 2x \cdot 2y + 2x \cdot 8 \][/tex]
Calculating these products, we get:
[tex]\[ 2x \cdot 2y = 4xy \][/tex]
[tex]\[ 2x \cdot 8 = 16x \][/tex]
Next, we distribute [tex]\(-2y\)[/tex] from [tex]\((2x - 2y)\)[/tex]:
[tex]\[ -2y \cdot 2y + -2y \cdot 8 \][/tex]
Calculating these products, we get:
[tex]\[ -2y \cdot 2y = -4y^2 \][/tex]
[tex]\[ -2y \cdot 8 = -16y \][/tex]
Now, we combine all the terms obtained through distribution:
[tex]\[ 4xy + 16x - 4y^2 - 16y \][/tex]
So after simplifying, we get:
[tex]\[ 4xy + 16x - 4y^2 - 16y \][/tex]
Therefore, the correct answer is:
A. [tex]\(4xy + 16x - 4y^2 - 16y\)[/tex]
