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

To rearrange and add the given monomials, we'll first group like terms and then combine them. 

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

Now, let's group the like terms together:

1. **Cubic terms in \( m \)**: 
   - \( m^3 \) from the first expression
   - \( 2m^3 \) from the second expression

   Sum: \( m^3 + 2m^3 = 3m^3 \)

2. **Terms with \( m^2n \)**:
   - \( 7m^2n \) from the first expression
   - \( 8m^2n \) from the second expression

   Sum: \( 7m^2n + 8m^2n = 15m^2n \)

3. **Terms with \( mn^2 \)**:
   - \( -6mn^2 \) from the first expression
   - \( -mn^2 \) from the second expression

   Sum: \( -6mn^2 - mn^2 = -7mn^2 \)

4. **Cubic terms in \( n \)**:
   - \( n^3 \) from the first expression
   - \( 2n^3 \) from the second expression

   Sum: \( n^3 + 2n^3 = 3n^3 \)

Now, let's write down the combined expression:

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

This is the final simplified expression after rearranging and adding the like terms.

Would you like more details or have any questions? Here are some related topics:

1. How to subtract monomials.
2. Understanding like terms in polynomials.
3. Simplifying polynomials with multiple variables.
4. Operations with polynomials in algebra.
5. Factoring polynomials after combining like terms.

**Tip:** Always ensure that you correctly identify and group like terms (terms with the same variables raised to the same powers) when simplifying expressions.

Learn how to rearrange and add monomials in polynomial expressions with this step-by-step guide. Explore the process of combining like terms and simplifying polynomial expressions. Suitable for students in Grades 7-9.

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