Question

use the associative property to determine which expression is equivalent

A. -3 x (4x x -2) x -6 = (-3 x 4x) x -2 - 6y
B. -3 x (4x x -2) x -6 = (-3 x 4x) (-2 x - 6y)
C. -3 x (4x x -2) x -6 = 18 - 8x
D. -3 x (4x x -2) x -6 = -7xy

Answer 1

To determine which expression is equivalent to \(-3 \times (4x \times -2) \times -6\) using the associative property, we'll begin by simplifying the left-hand side:

1. **Apply the associative property**: The associative property states that the grouping of numbers does not affect the product. We can calculate step by step:

\[
-3 \times (4x \times -2) \times -6
\]

First, calculate \(4x \times -2\):
\[
4x \times -2 = -8x
\]

Now substitute back into the expression:
\[
-3 \times (-8x) \times -6
\]

Calculate \(-3 \times -8x\):
\[
-3 \times -8x = 24x
\]

Then multiply by \(-6\):
\[
24x \times -6 = -144x
\]

So far we have simplified \(-3 \times (4x \times -2) \times -6\) to \(-144x\).

Now, let's evaluate each answer choice to see which one is equivalent to \(-144x\):

A. \((-3 \times 4x) \times -2 - 6y\):
\[
(-3 \times 4x) = -12x \implies -12x \times -2 = 24x, \text{ which does not equal } -144x
\]

B. \((-3 \times 4x) \times (-2 \times -6y)\):
\[
(-3 \times 4x) = -12x \implies (-2 \times -6y) = 12y \implies -12x \times 12y = -144xy, \text{ which is not equal to } -144x
\]

C. \(18 - 8x\):
This expression is linear but doesn't simplify to \(-144x\).

D. \(-7xy\):
This is a different expression and does not simplify to \(-144x\).

None of the options (A, B, C, or D) are equal to \(-144x\). Thus, it appears that none of the given options is correct. Please check the answer choices again.