-(-10n%5E3-12n-7n%5E2).jpeg "(-9n^2-5n^3-3n)-(-10n^3-12n-7n^2)")
Simplifying Polynomial Expressions: A Step-by-Step Guide
This article will guide you through the process of simplifying the polynomial expression: (-9n^2 - 5n^3 - 3n) - (-10n^3 - 12n - 7n^2).
Understanding the Process
Simplifying polynomial expressions involves combining like terms. Like terms are terms that have the same variable(s) raised to the same power.
Step 1: Distribute the Negative Sign
The minus sign in front of the second set of parentheses means we need to multiply each term inside the parentheses by -1.
- (-9n^2 - 5n^3 - 3n) + (10n^3 + 12n + 7n^2)
Step 2: Identify Like Terms
Identify terms with the same variable and exponent:
- -5n^3 and 10n^3 are like terms.
- -9n^2 and 7n^2 are like terms.
- -3n and 12n are like terms.
Step 3: Combine Like Terms
Combine the coefficients of like terms:
- (-5 + 10)n^3 = 5n^3
- (-9 + 7)n^2 = -2n^2
- (-3 + 12)n = 9n
Step 4: Write the Simplified Expression
Combine the simplified terms to get the final result:
5n^3 - 2n^2 + 9n
Conclusion
By following these simple steps, you can effectively simplify polynomial expressions. Remember to focus on identifying and combining like terms for a streamlined solution.