Question

Rewrite in simplest terms: minus, 6, left parenthesis, minus, 5, m, minus, 3, n, right parenthesis, plus, 8, n, minus, 3, left parenthesis, minus, 3, n, plus, 4, m, right parenthesis−6(−5m−3n)+8n−3(−3n+4m)

Answer 1

To simplify the expression \(-6(-5m - 3n) + 8n - 3(-3n + 4m)\), let's break it down step by step:

1. Distribute \(-6\) into \(-5m - 3n\):
\[
-6(-5m) + -6(-3n) = 30m + 18n
\]

2. Distribute \(-3\) into \(-3n + 4m\):
\[
-3(-3n) + -3(4m) = 9n - 12m
\]

3. Now, substitute these back into the expression:
\[
30m + 18n + 8n + 9n - 12m
\]

4. Combine like terms:
- For the \(m\) terms: \(30m - 12m = 18m\)
- For the \(n\) terms: \(18n + 8n + 9n = 35n\)

So, the simplified expression is:
\[
18m + 35n
\]