Sure! Let's simplify the expression [tex]\((2x - 2y)(2y + 8)\)[/tex] step-by-step.
1. Write Down the Expression:
[tex]\[
(2x - 2y)(2y + 8)
\][/tex]
2. Distribute Each Term in the First Parentheses to Each Term in the Second Parentheses:
To do this, use the distributive property (also known as the FOIL method for binomials):
[tex]\[
= 2x \cdot 2y + 2x \cdot 8 - 2y \cdot 2y - 2y \cdot 8
\][/tex]
3. Perform the Multiplications:
[tex]\[
= 4xy + 16x - 4y^2 - 16y
\][/tex]
4. Combine Like Terms (if any):
In this case, there are no like terms to combine.
Therefore, the simplified expression is:
[tex]\[
4xy + 16x - 4y^2 - 16y
\][/tex]
Now, let's compare this with the provided options:
A. [tex]\(4xy + 16x - 4y^2 - 16y\)[/tex]
B. [tex]\(4xy - 4y^2\)[/tex]
C. [tex]\(4xy - 16x - 4y^2 - 16y\)[/tex]
The correct answer is:
A. [tex]\(4xy + 16x - 4y^2 - 16y\)[/tex]
