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=−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 times negative 2 minus 6 y
−3⋅(4x⋅−2)⋅−6y=(−3⋅4x)(−2⋅−6y)
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=−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 times negative 2 minus 6 y
−3⋅(4x⋅−2)⋅−6y=(−3⋅4x)(−2⋅−6y)
Answers
GPT-4o mini
To analyze which expressions are equivalent using the Associative Property, we need to remember that the Associative Property allows us to group numbers in expressions differently without changing the outcome. The expressions can be simplified to determine their equivalence.
1. **Expression 1**: \(-3 \cdot (4x \cdot -2) \cdot -6y = 18 - 8x\)
2. **Expression 2**: \(-3 \cdot (4x \cdot -2) \cdot -6y = -7xy\)
3. **Expression 3**: \(-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x) \cdot -2 - 6y\)
4. **Expression 4**: \(-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x)(-2 \cdot -6y)\)
Now, let’s simplify the left side of the expressions, \(-3 \cdot (4x \cdot -2) \cdot -6y\):
1. Calculate \(4x \cdot -2\):
\(4x \cdot -2 = -8x\)
2. Then, calculate \(-3 \cdot (-8x) \cdot -6y\):
\(-3 \cdot -8x = 24x\)
Then, \(24x \cdot -6y = -144xy\)
So, we find that:
\(-3 \cdot (4x \cdot -2) \cdot -6y = -144xy\)
Now, let's check the right sides of each original expression:
- For **Expression 1**: \(18 - 8x\) ∼ \(-144xy\) (Not equivalent)
- For **Expression 2**: \(-7xy\) ∼ \(-144xy\) (Not equivalent)
- For **Expression 3**: \((-3 \cdot 4x) \cdot -2 - 6y\)
This simply doesn't form a single expression equal to \(-144xy\) (Not equivalent)
- For **Expression 4**: \((-3 \cdot 4x)(-2 \cdot -6y)\)
Let's break this down:
\((-3 \cdot 4x) = -12x\),
and \(-2 \cdot -6y = 12y\), hence \((-12x)(12y) = -144xy\)
The only equivalent expression here is **Expression 4**:
\[
-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x)(-2 \cdot -6y)
\]
So the final answer is:
- Expression 4 is equivalent.
1. **Expression 1**: \(-3 \cdot (4x \cdot -2) \cdot -6y = 18 - 8x\)
2. **Expression 2**: \(-3 \cdot (4x \cdot -2) \cdot -6y = -7xy\)
3. **Expression 3**: \(-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x) \cdot -2 - 6y\)
4. **Expression 4**: \(-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x)(-2 \cdot -6y)\)
Now, let’s simplify the left side of the expressions, \(-3 \cdot (4x \cdot -2) \cdot -6y\):
1. Calculate \(4x \cdot -2\):
\(4x \cdot -2 = -8x\)
2. Then, calculate \(-3 \cdot (-8x) \cdot -6y\):
\(-3 \cdot -8x = 24x\)
Then, \(24x \cdot -6y = -144xy\)
So, we find that:
\(-3 \cdot (4x \cdot -2) \cdot -6y = -144xy\)
Now, let's check the right sides of each original expression:
- For **Expression 1**: \(18 - 8x\) ∼ \(-144xy\) (Not equivalent)
- For **Expression 2**: \(-7xy\) ∼ \(-144xy\) (Not equivalent)
- For **Expression 3**: \((-3 \cdot 4x) \cdot -2 - 6y\)
This simply doesn't form a single expression equal to \(-144xy\) (Not equivalent)
- For **Expression 4**: \((-3 \cdot 4x)(-2 \cdot -6y)\)
Let's break this down:
\((-3 \cdot 4x) = -12x\),
and \(-2 \cdot -6y = 12y\), hence \((-12x)(12y) = -144xy\)
The only equivalent expression here is **Expression 4**:
\[
-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x)(-2 \cdot -6y)
\]
So the final answer is:
- Expression 4 is equivalent.