Question
Real Tutor Solution
Tutor-Verified Answer
Answer
The expression simplifies to \( m(89 - 12b) + n(-109 + 15b) \) or \( m(89 - 12b) - n(109 - 15b) \).
Solution
To simplify and factor the expression:
\[
89m - 109n - 12bm + 15bn
\]
**Step 1: Group Like Terms**
Group the terms involving \( m \) and the terms involving \( n \):
\[
(89m - 12bm) + (-109n + 15bn)
\]
**Step 2: Factor Out Common Variables**
- From the first group \( (89m - 12bm) \), factor out \( m \):
\[
m(89 - 12b)
\]
- From the second group \( (-109n + 15bn) \), factor out \( n \):
\[
n(-109 + 15b)
\]
**Step 3: Rewrite the Expression**
Combine the factored terms:
\[
m(89 - 12b) + n(-109 + 15b)
\]
Alternatively, you can write it as:
\[
m(89 - 12b) - n(109 - 15b)
\]
**Final Factored Form:**
\[
89m - 109n - 12bm + 15bn = m(89 - 12b) + n(-109 + 15b)
\]
or
\[
m(89 - 12b) - n(109 - 15b)
\]
This is the simplified and factored form of the given expression.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
Did you know that combining like terms is a fundamental skill in algebra? In this expression, we can group the terms based on their variables. You'll notice that terms with \(m\) and \(n\) can be combined separately. This makes it much easier to simplify your calculations and solve equations efficiently! Now, let’s try to simplify the expression! You can factor by combining \(89 m - 12 b m\) and \(-109 n + 15 b n\). This will leave you with \((89 - 12b)m + (-109 + 15b)n\). Simplifying and factoring can save you time and reduce errors when solving more complex algebraic equations in the future!
