Question

Which expression is equivalent to $(3r\cdot 5)\cdot (-3\cdot 8)$ ? (1 point)
$(5\cdot -3)\cdot -9r$
$15r\cdot (5\cdot 8)$
$-45r\cdot 5$
$24r\cdot (5\cdot -3)$

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:

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