Question

Use the Associative Property to determine which expressions are equivalent.(1 point) Responses −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=−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=(−3⋅4x)⋅−2−6y

Answer 1

To use the Associative Property to determine which expressions are equivalent, let's analyze the expressions provided. The Associative Property states that the way in which numbers are grouped in multiplication does not change the product.

The original expression is: \[ -3 \cdot (4x \cdot -2) \cdot -6y \]

Now, let's break down each response one at a time.

1. Response 1: \[ -3 \cdot (4x \cdot -2) \cdot -6y = 18 - 8x \] This is not equivalent since the left side is a multiplication expression, while the right side is a subtraction expression.

2. Response 2: \[ -3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x) \cdot (-2 \cdot -6y) \] This uses the associative and commutative properties and is therefore equivalent to the left side.

3. Response 3: \[ -3 \cdot (4x \cdot -2) \cdot -6y = -7xy \] This response makes a claim about the value being equal to \(-7xy\), which is not guaranteed to be true without evaluating both sides. So it's not demonstrably equivalent.

4. Response 4: \[ -3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x) \cdot -2 \cdot -6y \] This is correct as it also uses the associative property in a valid manner, making it equivalent.

Conclusion:

The expressions that are equivalent to the original expression using the Associative Property are Response 2 and Response 4.

Answer 2

which one is it

Answer 3

Based on the analysis of the expressions provided, both Response 2 and Response 4 correctly apply the Associative Property and are equivalent to the original expression \(-3 \cdot (4x \cdot -2) \cdot -6y\).

To summarize:

• Response 2: \(-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x) \cdot (-2 \cdot -6y)\) is equivalent.
• Response 4: \(-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x) \cdot -2 \cdot -6y\) is also equivalent.

If you need to pick only one response, Response 2 demonstrates the associative application more explicitly, but both responses are technically correct.