Answer :
To simplify the given expression [tex]\((2x - 2y)(2y + 8)\)[/tex], we need to use the distributive property (also known as the FOIL method for binomials). Here is a step-by-step solution:
1. Distribute each term in the first binomial to each term in the second binomial:
[tex]\[ (2x - 2y)(2y + 8) = 2x \cdot 2y + 2x \cdot 8 - 2y \cdot 2y - 2y \cdot 8 \][/tex]
2. Perform the multiplications:
[tex]\[ 2x \cdot 2y = 4xy \][/tex]
[tex]\[ 2x \cdot 8 = 16x \][/tex]
[tex]\[ -2y \cdot 2y = -4y^2 \][/tex]
[tex]\[ -2y \cdot 8 = -16y \][/tex]
3. Combine all the terms:
[tex]\[ 4xy + 16x - 4y^2 - 16y \][/tex]
So, the expression [tex]\((2x - 2y)(2y + 8)\)[/tex] simplifies to:
[tex]\[ 4xy + 16x - 4y^2 - 16y \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{4xy + 16x - 4y^2 - 16y} \][/tex]
Given the choices, the correct option is:
C. [tex]\(4 x y + 16 x - 4 y^2 - 16 y\)[/tex]
1. Distribute each term in the first binomial to each term in the second binomial:
[tex]\[ (2x - 2y)(2y + 8) = 2x \cdot 2y + 2x \cdot 8 - 2y \cdot 2y - 2y \cdot 8 \][/tex]
2. Perform the multiplications:
[tex]\[ 2x \cdot 2y = 4xy \][/tex]
[tex]\[ 2x \cdot 8 = 16x \][/tex]
[tex]\[ -2y \cdot 2y = -4y^2 \][/tex]
[tex]\[ -2y \cdot 8 = -16y \][/tex]
3. Combine all the terms:
[tex]\[ 4xy + 16x - 4y^2 - 16y \][/tex]
So, the expression [tex]\((2x - 2y)(2y + 8)\)[/tex] simplifies to:
[tex]\[ 4xy + 16x - 4y^2 - 16y \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{4xy + 16x - 4y^2 - 16y} \][/tex]
Given the choices, the correct option is:
C. [tex]\(4 x y + 16 x - 4 y^2 - 16 y\)[/tex]
