Question

Which expression is equivalent to (3r⋅5)⋅(−3⋅8) ?(1 point) Responses 15r⋅(5⋅8) 15 r times left parenthesis 5 times 8 right parenthesis 24r⋅(5⋅−3) 24 r times left parenthesis 5 times negative 3 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 \((3r \cdot 5) \cdot (-3 \cdot 8)\), let's break it down step by step.

1. First, simplify the multiplication inside the parentheses:

   • For the first part, \(3r \cdot 5 = 15r\).
   • For the second part, \(-3 \cdot 8 = -24\).

2. Now, combine these results: \[ (3r \cdot 5) \cdot (-3 \cdot 8) = 15r \cdot -24. \]

3. Finally, multiply these terms: \[ 15r \cdot -24 = -360r. \]

Now, let's analyze the provided response options:

1. 15r⋅(5⋅8): This equals \(15r \cdot 40\), which is not equal to \(-360r\).
2. 24r⋅(5⋅−3): This would equal \(24r \cdot (-15)\), which equals \(-360r\), so this is equivalent.
3. (5⋅−3)⋅−9r: This equals \(-15 \cdot -9r = 135r\), which is not equal to \(-360r\).
4. −45r⋅5: This equals \(-225r\), which is not equal to \(-360r\).

Therefore, the expression 24r⋅(5⋅−3) is equivalent to \((3r \cdot 5) \cdot (-3 \cdot 8)\).