Question

Which expression is equivalent to (3r⋅5)⋅(−3⋅8)(3r⋅5)⋅(−3⋅8) ?(1 point) Responses (5⋅−3)⋅−9r(5⋅−3)⋅−9r left parenthesis 5 times negative 3 right parenthesis times negative 9 r −45r⋅5−45r⋅5 negative 45 r times 5 15r⋅(5⋅8)15r⋅(5⋅8) 15 r times left parenthesis 5 times 8 right parenthesis 24r⋅(5⋅−3)

Answer 1

To simplify the expression \((3r \cdot 5) \cdot (-3 \cdot 8)\), we will break this down step by step.

1. **Calculate the individual parts**:
- First, calculate \(3r \cdot 5\):
\[
3r \cdot 5 = 15r
\]
- Next, calculate \(-3 \cdot 8\):
\[
-3 \cdot 8 = -24
\]

2. **Combine the results**:
Now, substitute these results back into the expression:
\[
(15r) \cdot (-24) = -360r
\]

We need to check the given options for something equivalent to \(-360r\).

Now let's look at the options:
1. **Option 1**: \((5 \cdot -3) \cdot -9r = (-15) \cdot -9r = 135r\) (Not equivalent)
2. **Option 2**: \(-45r \cdot 5 = -225r\) (Not equivalent)
3. **Option 3**: \(15r \cdot (5 \cdot 8) = 15r \cdot 40 = 600r\) (Not equivalent)
4. **Option 4**: \(24r \cdot (5 \cdot -3) = 24r \cdot -15 = -360r\) (Equivalent)

Thus, the correct equivalent expression is:
\[
\boxed{24r \cdot (5 \cdot -3)}
\]