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

Question

GPT-4o mini · Answer

To determine which expressions are equivalent using the Associative Property, we can look at the expressions you have provided:

$- 3 \cdot (4 x \cdot - 2) \cdot - 6 y$
$18 - 8 x$
$(- 3 \cdot 4 x) \cdot (- 2 \cdot - 6 y)$
$(- 3 \cdot 4 x) \cdot - 2 \cdot - 6 y$

The Associative Property states that when multiplying, the way we group the factors does not change the product.

Step 1: Simplifying the first expression:

$- 3 \cdot (4 x \cdot - 2) \cdot - 6 y$

Calculate $4 x \cdot - 2 = - 8 x$ . Then substitute:

$- 3 \cdot (- 8 x) \cdot (- 6 y) = - 3 \cdot 8 x y \cdot - 6 = 144 x y$

Step 2: Check against the other expressions.

For Expression 2: $18 - 8 x$ , we see that this expression is not equal to $144 x y$ .
For Expression 3: $(- 3 \cdot 4 x) \cdot (- 2 \cdot - 6 y)$

First, calculate $- 2 \cdot - 6 y = 12 y$ :

$(- 3 \cdot 4 x) \cdot 12 y = (- 12 x) \cdot 12 y = - 144 x y$

This also isn't equal to $144 x y$ .

For Expression 4: Starting with the same calculation:

$(- 3 \cdot 4 x) \cdot - 2 \cdot - 6 y = - 12 x \cdot - 6 y = 72 x y$

This is also not equal to $144 x y$ .

Step 3: Determine equivalences.

Among these expressions, we can see that:

Expressions 1 calculates to $144 x y$ .
Expression 3 calculates to $- 144 x y$ .
Expression 4 calculates to $72 x y$ .
Expression 2 is not equivalent either.

Since none of the expressions calculated to the same value, none of the provided expressions are equivalent.

The correct related expression here relies solely on the understanding of how multiplication groups via the Associative Property, but these specific results don't yield equivalency amongst the provided expressions.

In conclusion, based on our analysis and simplification, none of the original expressions are equivalent due to differing results.

Answer

U gotta pick lne

GPT-4o mini · Answer

I apologize for the confusion! Let's simplify and compare the expressions clearly.

Given the first expression:

$- 3 \cdot (4 x \cdot - 2) \cdot - 6 y$

We'll simplify it step by step:

$4 x \cdot - 2 = - 8 x$
So, $- 3 \cdot (- 8 x) \cdot - 6 y = 24 x y \cdot - 6 = - 144 x y$

Now let's evaluate the expressions:

Comparing the Expressions:

Expression 1: $- 3 \cdot (4 x \cdot - 2) \cdot - 6 y = - 144 x y$
Expression 2: $- 7 x y$ (not equal to $- 144 x y$ )
Expression 3: $(- 3 \cdot 4 x) \cdot (- 2 \cdot - 6 y)$
- Simplifying: $(- 3 \cdot 4 x) = - 12 x$ and $(- 2 \cdot - 6 y) = 12 y$
- So, $- 12 x \cdot 12 y = - 144 x y$ (this matches Expression 1)
Expression 4: $(- 3 \cdot 4 x) \cdot - 2 \cdot - 6 y$
- Again, $- 3 \cdot 4 x = - 12 x$
- Then we multiply: $- 12 x \cdot - 2 = 24 x$ and then $24 x \cdot - 6 y = - 144 x y$ (this also matches Expression 1).

Conclusion:

Thus, the equivalent expressions are:

Expression 1: $- 3 \cdot (4 x \cdot - 2) \cdot - 6 y$
Expression 3: $(- 3 \cdot 4 x) \cdot (- 2 \cdot - 6 y)$
Expression 4: $(- 3 \cdot 4 x) \cdot - 2 \cdot - 6 y$

Therefore, you can pick Expression 3 or Expression 4 as equivalent to Expression 1.

If you must pick one, I recommend Expression 3 because it clearly shows the associative grouping.