Question

Use the Associative Property to determine which expressions are equivalent.(1 point)
Responses

−3⋅(4x⋅−2)⋅−6y=−7xy
negative 3 times left parenthesis 4 x times negative 2 right parenthesis times negative 6 y equals negative 7 x y

−3⋅(4x⋅−2)⋅−6y=18−8x
negative 3 times left parenthesis 4 x times negative 2 right parenthesis times negative 6 y equals 18 minus 8 x

−3⋅(4x⋅−2)⋅−6y=(−3⋅4x)(−2⋅−6y)
negative 3 times left parenthesis 4 x times negative 2 right parenthesis times negative 6 y equals left parenthesis negative 3 times 4 x right parenthesis left parenthesis negative 2 times negative 6 y right parenthesis

−3⋅(4x⋅−2)⋅−6y=(−3⋅4x)⋅−2−6y

Answer 1

To determine which expressions are equivalent using the Associative Property, we can analyze the given equations one by one. The Associative Property states that the way numbers are grouped in multiplication does not affect the product.

1. **Expression 1**:
\(-3 \cdot (4x \cdot -2) \cdot -6y = -7xy\)

2. **Expression 2**:
\(-3 \cdot (4x \cdot -2) \cdot -6y = 18 - 8x\)

3. **Expression 3**:
\(-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x)(-2 \cdot -6y)\)

4. **Expression 4**:
\(-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x) \cdot -2 - 6y\)

### Step by Step Evaluation:

1. **Expression 1**: Checking if \(-3 \cdot (4x \cdot -2) \cdot -6y = -7xy\) holds:
Evaluate \(-3 \cdot (4x \cdot -2)\):
\[
-3 \cdot (4x \cdot -2) = 6x
\]
Thus,
\[
6x \cdot -6y = -36xy
\]
This does not equal \(-7xy\).

2. **Expression 2**: Checking if \(-3 \cdot (4x \cdot -2) \cdot -6y = 18 - 8x\) holds:
As shown above, \(-3 \cdot (4x \cdot -2) \cdot -6y = -36xy\), which does not equal \(18 - 8x\).

3. **Expression 3**: Checking if \(-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x)(-2 \cdot -6y)\):
Evaluate:
\[
(-3 \cdot (4x)) \cdot (-2 \cdot -6y) = (-12x)(12y) = 144xy
\]
Both sides equal 144xy, thus this expression is equivalent.

4. **Expression 4**: Checking if \(-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x) \cdot -2 - 6y\):
The left side simplifies as calculated to \(-36xy\). The right side simplifies to:
\[
(-12x) \cdot (-6y) = 72xy,
\]
which does not match \(-36xy\).

### Conclusion:
The only equivalent expression among the provided choices, based on the correct application of the Associative Property, is:

\(\boxed{(-3 \cdot 4x)(-2 \cdot -6y)}\) which is equivalent to the original expression.