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 find an expression equivalent to \((3r \cdot 5) \cdot (-3 \cdot 8)\), we can first calculate the values step by step.

1. Calculate \(3r \cdot 5\): \[ 3r \cdot 5 = 15r \]

2. Calculate \(-3 \cdot 8\): \[ -3 \cdot 8 = -24 \]

3. Combine these results: \[ (3r \cdot 5) \cdot (-3 \cdot 8) = 15r \cdot (-24) = -360r \]

Now, let’s analyze the response options provided:

1. Response 1: \(24r \cdot (5 \cdot -3)\)

   • This can be simplified to \(24r \cdot -15\) which gives \(-360r\). This is equivalent.

2. Response 2: \(15r \cdot (5 \cdot 8)\)

   • This is \(15r \cdot 40\) which simplifies to \(600r\). Not equivalent.

3. Response 3: \((5 \cdot -3) \cdot -9r\)

   • This is \(-15 \cdot -9r\) which simplifies to \(135r\). Not equivalent.

4. Response 4: \(-45r \cdot 5\)

   • This simplifies to \(-225r\). Not equivalent.

Thus, the equivalent expression is:

Response 1: \(24r \cdot (5 \cdot -3)\)