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

Question

?(1 point)
Responses

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

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

−45r⋅5

Answer 1

To simplify the expression \((3r \cdot 5) \cdot (-3 \cdot 8)\), we can follow these steps:

1. Calculate the inner products:

   • Multiply \(3r\) by \(5\) which gives \(15r\).
   • Multiply \(-3\) by \(8\) which gives \(-24\).

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

3. Multiply the coefficients: \[ 15r \cdot -24 = -360r \]

Now let's examine the options given:

1. Option 1: \((5 \cdot -3) \cdot -9r = (-15) \cdot -9r = 135r\)
2. Option 2: \(15r \cdot (5 \cdot 8) = 15r \cdot 40 = 600r\)
3. Option 3: \(24r \cdot (5 \cdot -3) = 24r \cdot -15 = -360r\) (this matches our calculated value)
4. Option 4: \(-45r \cdot 5 = -225r\)

The expression equivalent to \((3r \cdot 5) \cdot (-3 \cdot 8)\) is:

Option 3: \(24r \cdot (5 \cdot -3)\).