(−5v3−9v2+6v)−(−5v3+9v2−6v)

Jasonbradley

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Jun 17, 2024

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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

1. 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)

2. Combine like terms:

   Now, group together the terms with the same variable and exponent:

   (-5v3 + 5v3) + (-9v2 - 9v2) + (6v + 6v)

3. Simplify:

   Add the coefficients of each group of like terms:

   0 + (-18v2) + (12v)

4. 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.