Which expression is equivalent to (3r⋅5)⋅(−3⋅8)

Question

?(1 point)
Responses

24r⋅(5⋅−3)
24 r times left parenthesis 5 times negative 3 right parenthesis

15r⋅(5⋅8)
15 r times left parenthesis 5 times 8 right parenthesis

(5⋅−3)⋅−9r
left parenthesis 5 times negative 3 right parenthesis times negative 9 r

−45r⋅5

Answer 1

To simplify the expression \((3r \cdot 5) \cdot (-3 \cdot 8)\), we can first calculate each part step by step:

1. Calculate \(3r \cdot 5 = 15r\).
2. Calculate \(-3 \cdot 8 = -24\).

Now, put both parts together:

\[ (3r \cdot 5) \cdot (-3 \cdot 8) = 15r \cdot (-24). \]

Now, multiply \(15r\) and \(-24\):

\[ 15r \cdot (-24) = -360r. \]

Now, let's check the options:

1. 24r⋅(5⋅−3) simplifies to \(24r \cdot -15 = -360r\) (correct).
2. 15r⋅(5⋅8) simplifies to \(15r \cdot 40 = 600r\) (incorrect).
3. (5⋅−3)⋅−9r is equal to \(-15 \cdot -9r = 135r\) (incorrect).
4. −45r⋅5 simplifies to \(-225r\) (incorrect).

So the equivalent expression is:

24r⋅(5⋅−3).