Question

Which algebraic expression is equivalent to the expression below?

8(4x - 2)
A.
4x - 16
B.
8x - 6
C.
32x + 16
D.
32x - 16

Answer 1

To find an algebraic expression equivalent to \( 8(4x - 2) \), we can apply the distributive property. This involves multiplying \( 8 \) by each term inside the parentheses:

\[
8(4x - 2) = 8 \cdot 4x + 8 \cdot (-2)
\]

Calculating each term:

1. \( 8 \cdot 4x = 32x \)
2. \( 8 \cdot (-2) = -16 \)

Now, combine these results:

\[
8(4x - 2) = 32x - 16
\]

Now, we can compare it with the options given:

A. \( 4x - 16 \)
B. \( 8x - 6 \)
C. \( 32x + 16 \)
D. \( 32x - 16 \)

The correct answer is:

**D. \( 32x - 16 \)**.