Question

Use the Associative Property to determine which expressions are equivalent.
−3⋅(4x⋅−2)⋅−6y=−7xy

−3⋅(4x⋅−2)⋅−6y=(−3⋅4x)(−2⋅−6y)

−3⋅(4x⋅−2)⋅−6y=(−3⋅4x)⋅−2−6y

−3⋅(4x⋅−2)⋅−6y=18−8x

Answer 1

To determine which expressions are equivalent using the Associative Property of multiplication, we can analyze the given expressions.

The **Associative Property** states that when multiplying numbers, the way in which the numbers are grouped does not affect the product. In other words, \( (a \cdot b) \cdot c = a \cdot (b \cdot c) \).

Let's break down the expressions given:

1. **Given Expression**:
\[
-3 \cdot (4x \cdot -2) \cdot -6y
\]

2. **First Comparison**:
\[
-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x)(-2 \cdot -6y)
\]
This applies the associative property correctly by regrouping the factors. So this statement is **true**.

3. **Second Comparison**:
\[
-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x) \cdot -2 - 6y
\]
This statement is incorrect as it uses the wrong operations (it introduces a subtraction instead of multiplying). So this statement is **false**.

4. **Third Comparison**:
\[
-3 \cdot (4x \cdot -2) \cdot -6y = 18 - 8x
\]
This statement seems to equate an expression involving multiplication to one involving addition and seems incorrect. Therefore, this statement is also **false**.

### Conclusion:
The only correct equivalent expression using the associative property is the first comparison:
\[
-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x)(-2 \cdot -6y).
\]

The other two comparisons are not equivalent.