Question

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

−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
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=−7xy

Answer 1

To determine which expressions are equivalent using the Associative Property, let's analyze each expression step by step. The Associative Property of multiplication states that the grouping of factors does not change the product. Therefore, we can regroup the factors as needed.

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

This expression is equivalent. We can regroup the terms correctly, and since multiplication is associative, this holds true.

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

This is **not** equivalent since it's incorrectly combining multiplication and subtraction, which doesn't relate to associative grouping.

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

This expression is also **not** equivalent because it's not following the associative property and also includes an incorrect operation of subtraction.

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

Again, this expression is **not** equivalent as it states a relationship that cannot be established through associativity.

In conclusion, **Expression 1** is equivalent, while the other expressions are not equivalent.