Which expression is equivalent to $(3r\cdot 5)\cdot (-3\cdot 8)$ ? (1 point)

Question

$(5\cdot -3)\cdot -9r$
$15r\cdot (5\cdot 8)$
$-45r\cdot 5$
$24r\cdot (5\cdot -3)$

Answer 1

To simplify the expression \((3r \cdot 5) \cdot (-3 \cdot 8)\), we will break it down step by step.

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

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

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

4. Break down the multiplication: \[ 15r \cdot (-24) = -360r \]

Now, let's consider the options provided:

• \((5 \cdot -3) \cdot -9r\): This does not match our result.
• \(15r \cdot (5 \cdot 8)\): This simplifies to \(15r \cdot 40 = 600r\), which does not match.
• \(-45r \cdot 5\): This simplifies to \(-225r\), which does not match.
• \(24r \cdot (5 \cdot -3)\): The expression inside the parentheses is \(5 \cdot -3 = -15\), leading to \(24r \cdot -15 = -360r\), which matches our result.

Thus, the equivalent expression is:

\[ \boxed{24r \cdot (5 \cdot -3)} \]