simplify (3mn + 2n2 − 3m2) + (4m2 − 2n2 + 6mn)

Let's simplify the expression \((3mn + 2n^2 − 3m^2) + (4m^2 − 2n^2 + 6mn)\).

1. **Group like terms:**
   \[
   (3mn + 6mn) + (2n^2 - 2n^2) + (-3m^2 + 4m^2)
   \]

2. **Simplify each group:**
   - \(3mn + 6mn = 9mn\)
   - \(2n^2 - 2n^2 = 0\)
   - \(-3m^2 + 4m^2 = m^2\)

3. **Combine the simplified terms:**
   \[
   9mn + m^2
   \]

So, the simplified expression is:

\[
m^2 + 9mn
\]

Would you like more details or have any questions?

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**Related Questions:**
1. How would you factor the expression \(m^2 + 9mn\)?
2. What if the expression had a subtraction sign between the two groups instead of addition?
3. Can you expand and simplify \( (m + 3n)(m + 3n) \)?
4. How does the distributive property apply in simplifying expressions like this?
5. What happens if one of the variables in the expression equals zero?

**Tip:** When simplifying expressions, always combine like terms, which are terms with the same variables raised to the same power.

Learn how to simplify the expression (3mn + 2n^2 − 3m^2) + (4m^2 − 2n^2 + 6mn) step-by-step with this detailed solution. This problem covers key algebraic concepts, including simplifying expressions and combining like terms. Suitable for students in Grades 7-9.

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