Subtraction of monomial Rearrange and add this following
m^3 + 7m^n -6mn^, 2m^3 + 8m^n - mn^ + 2n^3

To solve the problem, let's first identify and group like terms. You are provided with the following two expressions:

1. \( m^3 + 7m^n - 6mn \)
2. \( 2m^3 + 8m^n - mn + 2n^3 \)

### Step 1: Rearrange the expressions by grouping like terms:
- Combine like terms:
  - For \( m^3 \): \( m^3 \) from the first expression and \( 2m^3 \) from the second.
  - For \( m^n \): \( 7m^n \) from the first expression and \( 8m^n \) from the second.
  - For \( mn \): \( -6mn \) from the first expression and \( -mn \) from the second.
  - For \( n^3 \): There is no \( n^3 \) term in the first expression, but there is \( 2n^3 \) in the second.

### Step 2: Add the corresponding terms:
1. \( m^3 + 2m^3 = 3m^3 \)
2. \( 7m^n + 8m^n = 15m^n \)
3. \( -6mn - mn = -7mn \)
4. \( 2n^3 \) (no like term from the first expression)

### Final Expression:
The sum of the two expressions is:

\[
3m^3 + 15m^n - 7mn + 2n^3
\]

This expression is fully simplified.

### Do you want more details or have any questions? 

Here are 5 related questions to practice:

1. Simplify: \( 4x^2 + 5xy - 3y^2 + 2x^2 + 6xy + y^2 \)
2. Subtract: \( 3a^2 + 7ab - 2b^2 \) from \( 5a^2 + 9ab - 4b^2 \)
3. Add: \( 2p^3 + 3p^2q + 4pq^2 + 5q^3 \) and \( p^3 - p^2q + pq^2 - q^3 \)
4. Combine: \( 4m^2n - 3mn^2 + 2mn \) and \( 7m^2n + 5mn^2 - 9mn \)
5. Simplify: \( 6x^3 - 4x^2 + 2x - 7x^3 + 5x^2 - 3x \)

**Tip:** When combining like terms, ensure you only add or subtract coefficients of terms that have exactly the same variables raised to the same powers.

Explore a detailed solution for subtracting monomials and rearranging expressions. Learn how to combine like terms effectively with step-by-step examples. Suitable for Grades 7-9 students studying algebra and polynomial operations.

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