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

Question

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=(−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
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 times negative 2 minus 6 y

−3⋅(4x⋅−2)⋅−6y=18−8x

Answer 1

To use the Associative Property to determine which expressions are equivalent, we need to analyze each of the given statements based on the property, which states that the way in which numbers are grouped in multiplication does not change their product.

Let's evaluate each expression:

1. Expression: \(-3 \cdot (4x \cdot -2) \cdot -6y = -7xy\)
   Analysis: This equation is not obviously equivalent because the left side simplifies to a different product than the right side, particularly since there are no operations that lead directly to \(-7xy\).

2. Expression: \(-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x)(-2 \cdot -6y)\)
   Analysis: This expression uses the Associative Property correctly since both sides can be simplified to find the same resulting value. Therefore, this equality holds.

3. Expression: \(-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x) \cdot -2 - 6y\)
   Analysis: This expression does not hold because it incorrectly represents the distribution. The expression on the right side introduces an error in operation, as the original multiplication is not being maintained.

4. Expression: \(-3 \cdot (4x \cdot -2) \cdot -6y = 18 - 8x\)
   Analysis: This expression also does not hold because the left side would not simplify to equal \(18 - 8x\).

Based on the analysis, the expression that correctly uses the Associative Property in an equivalent form is: \(-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x)(-2 \cdot -6y)\).