Question

Use the Associative Property to determine which expressions are equivalent.

-3 times (4x times -2) times -6y = (-3 times 4x) times -2 - 6y

-3 times (4x times -2) times -6y = (-3 times 4x) (-2 times 6y)

-3 times (4x times -2) times -6y = -7xy

-3 times (4x times -2) times -6y = 18 - 8x

Answer 1

To determine which expressions are equivalent using the Associative Property, we first need to simplify the left side of the first expression, \(-3 \times (4x \times -2) \times -6y\).

1. **Simplify the left side:**
\[
-3 \times (4x \times -2) \times -6y
\]
Start with \(4x \times -2\):
\[
4x \times -2 = -8x
\]
Now substitute that back into the expression:
\[
-3 \times (-8x) \times -6y
\]
Next, simplify \(-3 \times -8x\):
\[
-3 \times -8x = 24x
\]
Now, multiply by \(-6y\):
\[
24x \times -6y = -144xy
\]

So, the left side simplifies to \(-144xy\).

Now let's analyze the right side of each expression to see if any of them simplify to \(-144xy\).

### Expressions to Evaluate:

1. **First Expression:**
\[
(-3 \times 4x) \times -2 - 6y
\]
This can be interpreted as:
\[
(-12x) \times -2 - 6y = 24x - 6y
\]
This does not equal \(-144xy\).

2. **Second Expression:**
\[
(-3 \times 4x) \times (-2 \times 6y)
\]
First calculate \( -2 \times 6y = -12y\):
\[
(-12x) \times -12y = 144xy
\]
This does not equal \(-144xy\).

3. **Third Expression:**
\[
-7xy
\]
This clearly does not equal \(-144xy\).

4. **Fourth Expression:**
\[
18 - 8x
\]
This does not equal \(-144xy\).

### Summary of Evaluation:
None of the given expressions simplify to \(-144xy\).

Thus, none of the expressions are equivalent to the left side.