Question

Use the Associative Property to determine which expressions are equivalent.(1 point)%0D%0AResponses%0D%0A%0D%0A−3⋅(4x⋅−2)⋅−6y=18−8x%0D%0Anegative 3 times left parenthesis 4 x times negative 2 right parenthesis times negative 6 y equals 18 minus 8 x%0D%0A%0D%0A−3⋅(4x⋅−2)⋅−6y=−7xy%0D%0Anegative 3 times left parenthesis 4 x times negative 2 right parenthesis times negative 6 y equals negative 7 x y%0D%0A%0D%0A−3⋅(4x⋅−2)⋅−6y=(−3⋅4x)(−2⋅−6y)%0D%0Anegative 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%0D%0A%0D%0A−3⋅(4x⋅−2)⋅−6y=(−3⋅4x)⋅−2−6y

Answer 1

write the correct expression

Answer 2

To determine which expressions are equivalent using the Associative Property, we need to analyze the expressions you provided.

### 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:
\[
-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x)(-2 \cdot -6y)
\]

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

### Analysis of Expressions:

#### Expression 1 vs. 2:
To check if the left-hand side equals the right-hand side, we need to perform the calculations.

1. Calculate the left-hand side:
\(-3 \cdot (4x \cdot -2) \cdot -6y\)

- Calculate \(4x \cdot -2 = -8x\)
- Now, calculate \(-3 \cdot -8x \cdot -6y = -3 \cdot -8 \cdot -6 \cdot xy = 144xy\) (disregarding signs for a moment).

Now consider the right-hand sides:
- For \(18 - 8x\), we can't equate this with \(144xy\).
- For \(-7xy\), again, we don't get a match with \(144xy\).

#### Expression 3:
The left-hand side and right-hand side expr (-3 \cdot (4x \cdot -2) \cdot -6y)
become \((-3 \cdot 4x)(-2 \cdot -6y)\) respectively.

- Calculate (\(-3 \cdot 4x) = -12x)\)
- Now calculate \(-2 \cdot -6y = 12y\)
- So we have \((-12x)(12y) = -144xy\).

Therefore, this expression does equate well.

#### Expression 4:
\((-3 \cdot 4x) \cdot -2 \cdot -6y\)
- First, \(-3 \cdot 4x = -12x\)
- Then \(-12x \cdot -2 = 24x\)
- Finally, \(24x \cdot -6y = -144xy\).

Both Expression 3 and Expression 4 yield \(-144xy\) on the left.

### Conclusion:
Based on this analysis using the Associative Property, Expressions 3 and 4 are equivalent because they result in the same calculation, whereas Expressions 1 and 2 are not equivalent.

Answer 3

To write the correct expression based on the calculations and comparisons we've done, we are primarily focusing on ensuring that we find an equivalent expression based on the left-hand side.

The original expression we started with is:
\[
-3 \cdot (4x \cdot -2) \cdot -6y
\]

From our calculations, we identified two expressions that are equivalent to the left-hand side, which results in \(-144xy\):

1. Using the Associative Property:
\[
(-3 \cdot 4x)(-2 \cdot -6y) = (-12x)(12y) = -144xy
\]

2. Also:
\[
(-3 \cdot 4x) \cdot -2 \cdot -6y = (-12x) \cdot -2 \cdot -6y = -144xy
\]

So, we can express the equivalence clearly:

The correct equivalent expression can be stated as:
\[
-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x)(-2 \cdot -6y) = (-3 \cdot 4x) \cdot -2 \cdot -6y = -144xy
\]

If you want it in an algebraic form, you could simply state:
\[
-3 \cdot (4x \cdot -2) \cdot -6y = -144xy
\]

This conveys the equivalence concisely.