Question

Which of the following is equivalent to 4(2 − x) + 2x(2 − x)?

Answer 1

To simplify the expression \( 4(2 - x) + 2x(2 - x) \), we will distribute the terms step by step.

First, distribute \( 4 \) in the first term:
\[
4(2 - x) = 4 \cdot 2 - 4 \cdot x = 8 - 4x
\]

Next, distribute \( 2x \) in the second term:
\[
2x(2 - x) = 2x \cdot 2 - 2x \cdot x = 4x - 2x^2
\]

Now, we can combine the two results:
\[
8 - 4x + 4x - 2x^2
\]

The \(-4x\) and \(4x\) terms cancel each other out:
\[
8 - 2x^2
\]

Thus, the expression \( 4(2 - x) + 2x(2 - x) \) simplifies to:
\[
\boxed{8 - 2x^2}
\]