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

To solve this problem, let's first clarify the terms and their coefficients before rearranging and combining like terms. The given expression is:

\[ (m^3 + 7m^n - 6mn) + (2m^3 + 8m^n - mn + 2n^3) \]

Now, let's group and add the like terms:

1. **Terms involving \(m^3\):**
   \[
   m^3 + 2m^3 = 3m^3
   \]

2. **Terms involving \(m^n\):**
   \[
   7m^n + 8m^n = 15m^n
   \]

3. **Terms involving \(mn\):**
   \[
   -6mn - mn = -7mn
   \]

4. **Terms involving \(n^3\):**
   \[
   2n^3 
   \]
   (There is no other \(n^3\) term to combine with.)

After combining all like terms, the expression becomes:

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

This is the final simplified expression.

Would you like further details or have any questions?

Here are 5 related questions to explore:

1. How do you combine like terms in polynomials?
2. What is the significance of the degree of a term in a polynomial?
3. Can you subtract or add polynomials that have different variables?
4. How does the distributive property apply to polynomial expressions?
5. What happens when you multiply two polynomials together?

**Tip:** Always align like terms (terms with the same variable and exponent) vertically when adding or subtracting polynomials to avoid mistakes.

Learn how to subtract and simplify monomials and polynomials with this step-by-step guide. The problem involves rearranging and combining like terms in algebraic expressions, focusing on monomials such as m^3, m^n, mn, and n^3. Suitable for high school students studying algebra.

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