Question
Use the Associative Property to determine which expressions are equivalent.(1 point) Responses -3\cdot\left(4x\cdot-2\right)\cdot-6y=\left(-3\cdot4x\right)\cdot-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\cdot\left(4x\cdot-2\right)\cdot-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\cdot\left(4x\cdot-2\right)\cdot-6y=-7xy negative 3 times left parenthesis 4 x times negative 2 right parenthesis times negative 6 y equals negative 7 x y -3\cdot\left(4x\cdot-2\right)\cdot-6y=\left(-3\cdot4x\right)\left(-2\cdot-6y\right)
Answers
GPT-4o mini
To determine which expressions are equivalent using the Associative Property, we need to understand that the Associative Property allows us to regroup numbers in addition and multiplication without changing the final result. In this case, we are dealing with multiplication.
The original expression is:
\[
-3 \cdot (4x \cdot -2) \cdot -6y
\]
Now let's examine the responses you provided to see if any of them are equivalent to this expression.
1. \( \left(-3 \cdot 4x\right) \cdot -2 \cdot -6y \)
- This expression is equivalent because we can regroup the terms using the Associative Property.
2. \( 18 - 8x \)
- This expression is numerical and does not reflect the original expression involving variables, so it is not equivalent.
3. \( -7xy \)
- This expression simplifies to a single product involving \(x\) and \(y\), and does not match the original expression, so it is not equivalent.
4. \( \left(-3 \cdot 4x\right) \cdot (-2 \cdot -6y) \)
- This expression is also equivalent because we can regroup the terms according to the Associative Property.
Based on the analysis:
- The first and fourth responses are equivalent to the original expression.
- The second and third responses are not equivalent.
The original expression is:
\[
-3 \cdot (4x \cdot -2) \cdot -6y
\]
Now let's examine the responses you provided to see if any of them are equivalent to this expression.
1. \( \left(-3 \cdot 4x\right) \cdot -2 \cdot -6y \)
- This expression is equivalent because we can regroup the terms using the Associative Property.
2. \( 18 - 8x \)
- This expression is numerical and does not reflect the original expression involving variables, so it is not equivalent.
3. \( -7xy \)
- This expression simplifies to a single product involving \(x\) and \(y\), and does not match the original expression, so it is not equivalent.
4. \( \left(-3 \cdot 4x\right) \cdot (-2 \cdot -6y) \)
- This expression is also equivalent because we can regroup the terms according to the Associative Property.
Based on the analysis:
- The first and fourth responses are equivalent to the original expression.
- The second and third responses are not equivalent.