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=−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=18−8x
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=−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=18−8x
Answers
GPT-4o mini
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 says that when three or more numbers are multiplied, the product is the same regardless of the grouping of the numbers. For example, \((a \cdot b) \cdot c = a \cdot (b \cdot c)\).
Let's analyze the statements:
1. **−3⋅(4x⋅−2)⋅−6y=(−3⋅4x)(−2⋅−6y)**:
This expression is using the property correctly by grouping the terms differently. This is equivalent as multiplication is associative.
2. **−3⋅(4x⋅−2)⋅−6y=(−3⋅4x)⋅−2−6y**:
This expression is not equivalent since \((-3 \cdot 4x) \cdot -2 - 6y\) is not the same as multiplying all three terms together.
3. **−3⋅(4x⋅−2)⋅−6y=−7xy**:
This statement does not show equivalence without simplification. You would need to simplify the left side to see if it equals \(-7xy\), which involves actual calculations.
4. **−3⋅(4x⋅−2)⋅−6y=18−8x**:
Again, this does not state equivalence without simplification or evaluation.
Final answer: The first expression **(−3⋅(4x⋅−2)⋅−6y=(−3⋅4x)(−2⋅−6y))** is equivalent by the Associative Property. The other expressions need further evaluation or simplification to determine their equivalence.
Let's analyze the statements:
1. **−3⋅(4x⋅−2)⋅−6y=(−3⋅4x)(−2⋅−6y)**:
This expression is using the property correctly by grouping the terms differently. This is equivalent as multiplication is associative.
2. **−3⋅(4x⋅−2)⋅−6y=(−3⋅4x)⋅−2−6y**:
This expression is not equivalent since \((-3 \cdot 4x) \cdot -2 - 6y\) is not the same as multiplying all three terms together.
3. **−3⋅(4x⋅−2)⋅−6y=−7xy**:
This statement does not show equivalence without simplification. You would need to simplify the left side to see if it equals \(-7xy\), which involves actual calculations.
4. **−3⋅(4x⋅−2)⋅−6y=18−8x**:
Again, this does not state equivalence without simplification or evaluation.
Final answer: The first expression **(−3⋅(4x⋅−2)⋅−6y=(−3⋅4x)(−2⋅−6y))** is equivalent by the Associative Property. The other expressions need further evaluation or simplification to determine their equivalence.