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

Responses

−3⋅(4x⋅−2)⋅−6y=−7xy

−3⋅(4x⋅−2)⋅−6y=(−3⋅4x)(−2⋅−6y)

−3⋅(4x⋅−2)⋅−6y=18−8x

−3⋅(4x⋅−2)⋅−6y=(−3⋅4x)⋅−2−6y

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 months ago

To determine which expressions are equivalent using the Associative Property, we first need to understand what the Associative Property states. The Associative Property of multiplication indicates that the way in which factors are grouped does not change the product. In other words:

- \(a \cdot (b \cdot c) = (a \cdot b) \cdot c\)

Now, let's analyze the given responses one by one:

1. **\(-3 \cdot (4x \cdot -2) \cdot -6y = -7xy\)**
This statement does not seem valid as we cannot directly equate this product to \(-7xy\) without further computations.

2. **\(-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x)(-2 \cdot -6y)\)**
This uses the Associative Property correctly because it is simply regrouping the factors in a different way. This statement is true.

3. **\(-3 \cdot (4x \cdot -2) \cdot -6y = 18 - 8x\)**
This statement does not hold true as \(-3 \cdot (4x \cdot -2) \cdot -6y\) is a multiplication result, while \(18 - 8x\) is a polynomial expression. They cannot be equivalent.

4. **\(-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x) \cdot -2 - 6y\)**
This expression does not use the Associative Property correctly. Also, the right side seems incorrect as well since the left side is a product and not a sum.

Given the analysis above, the only expression that correctly shows the use of the Associative Property is:

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