Simplifying Polynomial Expressions
This article will guide you through simplifying the expression (−5v3−9v2+6v)−(−5v3+9v2−6v).
Understanding the Concept
The expression involves combining like terms. Like terms are terms that have the same variable and exponent. For example, 5v3 and 5v3 are like terms, while 9v2 and 6v are not.
Simplifying the Expression

Distribute the negative sign:
The minus sign in front of the second set of parentheses means we multiply each term inside the parentheses by 1:
(−5v3−9v2+6v) + (5v3  9v2 + 6v)

Combine like terms:
Now, group together the terms with the same variable and exponent:
(5v3 + 5v3) + (9v2  9v2) + (6v + 6v)

Simplify:
Add the coefficients of each group of like terms:
0 + (18v2) + (12v)

Final Result:
The simplified expression is 18v2 + 12v.
Conclusion
By following the steps above, we have successfully simplified the expression (−5v3−9v2+6v)−(−5v3+9v2−6v) to 18v2 + 12v. This process is crucial for solving algebraic equations and manipulating polynomials in various mathematical applications.