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

Let's start by rewriting the given expression clearly and correctly identify each term:

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

Now, let's subtract the second polynomial from the first one:

### Step 1: Distribute the negative sign
We need to distribute the negative sign across the second polynomial:

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

### Step 2: Combine like terms

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

2. **Terms involving \(m^3n\) (if this was meant as \(m^3n\) instead of \(m^n\)):**
   \[
   7m^3n 
   \]
   (There is no corresponding term to subtract from.)

3. **Terms involving \(mn\):**
   \[
   -6mn + mn = -5mn
   \]

4. **Terms involving \(m^n\):**
   \[
   -8m^n
   \]
   (There is no corresponding term to subtract from.)

5. **Terms involving \(n^3\):**
   \[
   -2n^3
   \]
   (There is no corresponding term to subtract from.)

### Final Simplified Expression:
\[
-m^3 + 7m^3n - 5mn - 8m^n - 2n^3
\]

This is the final simplified expression after subtraction.

Would you like further details or have any questions?

Here are 5 related questions to explore:

1. What is the process for subtracting polynomials?
2. How do you determine which terms are like terms when combining?
3. What is the importance of correctly distributing the negative sign in polynomial subtraction?
4. How does the degree of a term affect its placement in a polynomial?
5. Can you explain the difference between adding and subtracting polynomials?

**Tip:** When subtracting polynomials, always remember to distribute the negative sign to each term in the polynomial being subtracted.

Learn how to subtract polynomials step-by-step: (m^3 + 7m^3n - 6mn) - (2m^3 + 8m^n - mn + 2n^3). Understand how to distribute the negative sign and combine like terms in polynomial subtraction. Suitable for Grades 7-9.

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