(-10mn^3-4n^4)-(-2n^4-7mn^3-6n^3)-(5n^3+6mn^3)

2 min read Jun 16, 2024

Simplifying the Polynomial Expression

This article will guide you through simplifying the polynomial expression: (-10mn^3-4n^4)-(-2n^4-7mn^3-6n^3)-(5n^3+6mn^3). We'll break down each step to ensure clarity and understanding.

Step 1: Distribute the Negative Signs

First, we need to distribute the negative signs in front of the parentheses. Remember, multiplying a negative sign by a negative sign results in a positive sign.

(-10mn^3-4n^4) + (2n^4 + 7mn^3 + 6n^3) + (-5n^3 - 6mn^3)

Step 2: Combine Like Terms

Now, we can combine the terms with the same variables and exponents.

n^4 terms: -4n^4 + 2n^4 = -2n^4
n^3 terms: 6n^3 - 5n^3 = n^3
mn^3 terms: -10mn^3 + 7mn^3 - 6mn^3 = -9mn^3

Step 3: Write the Simplified Expression

Finally, we put the combined terms together to get the simplified expression.

-2n^4 + n^3 - 9mn^3

Conclusion

By following these steps, we have successfully simplified the polynomial expression (-10mn^3-4n^4)-(-2n^4-7mn^3-6n^3)-(5n^3+6mn^3) to -2n^4 + n^3 - 9mn^3. Remember, understanding the order of operations and how to combine like terms is crucial for simplifying polynomial expressions.