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 open paren 4 x minus 2 close paren times negative 6 y is equal to open paren negative 3 times 4 x close paren times negative 2 minus 6 y

−3⋅(4x−2)⋅−6y=−7xy
negative 3 times open paren 4 x minus 2 close paren times negative 6 y is equal to negative 7 x y

−3⋅(4x−2)⋅−6y=(−3⋅4x)(−2⋅−6y)
negative 3 times open paren 4 x minus 2 close paren times negative 6 y is equal to open paren negative 3 times 4 x close paren times open paren negative 2 times negative 6 y close paren

−3⋅(4x−2)⋅−6y=18−8x

Answer 1

To determine which expressions are equivalent using the Associative Property, we first need to simplify the left side of each given expression:

**Left Side:**
\[
-3 \cdot (4x - 2) \cdot -6y
\]

Using the Associative Property, we can regroup and simplify:
\[
= (-3 \cdot -6y) \cdot (4x - 2)
\]
\[
= 18y \cdot (4x - 2)
\]
\[
= 18y \cdot 4x - 18y \cdot 2
\]
\[
= 72xy - 36y
\]

Now let's compare this with the options:

1. **Option 1:**
\[
(−3 \cdot 4x) \cdot -2 - 6y
\]
Simplifying this:
\[
= -12x \cdot -2 - 6y = 24x - 6y \quad (Not equivalent)
\]

2. **Option 2:**
\[
-7xy
\]
(Not equivalent to \(72xy - 36y\))

3. **Option 3:**
\[
(−3 \cdot 4x)(−2 \cdot -6y)
\]
Simplifying this:
\[
= -12x \cdot 12y = 144xy \quad (Not equivalent to \(72xy - 36y\))
\]

4. **Option 4:**
\[
18 - 8x
\]
(Not equivalent to \(72xy - 36y\))

After evaluating all options, none of the given expressions are equivalent to the simplified version of the left side \(72xy - 36y\).

In conclusion, none of the responses provided are equivalent to \(-3 \cdot (4x - 2) \cdot -6y\).