Which expression is equivalent to (3r⋅5)⋅(−3⋅8) ?(1 point)

Question

Responses

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

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

−45r⋅5

Answer 1

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

Let's start by simplifying the expression:

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

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

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

Now let's look at the options provided:

1. \( 15r \cdot (5 \cdot 8) \): \( 5 \cdot 8 = 40 \), so this is \( 15r \cdot 40 = 600r \), which is not equal to \(-360r\).

2. \( (5 \cdot -3) \cdot -9r \): \( 5 \cdot -3 = -15 \), so this becomes \( -15 \cdot -9r = 135r \), which is not equal to \(-360r\).

3. \( 24r \cdot (5 \cdot -3) \): \( 5 \cdot -3 = -15 \), so this gives \( 24r \cdot -15 = -360r \), which is equal to our original calculation.

4. \( -45r \cdot 5 \): This evaluates to \( -225r \), which is also not equal to \(-360r\).

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