(3-2x+2x^2)+(4x-5+3x^2)

Jasonbradley

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Jun 16, 2024

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Simplifying Polynomial Expressions: (3-2x+2x^2)+(4x-5+3x^2)

This article will guide you through the process of simplifying the polynomial expression (3-2x+2x^2)+(4x-5+3x^2).

Understanding the Steps

1. Identify Like Terms:

   • Like terms are terms that have the same variable and the same exponent.
   • In our expression, we have the following like terms:
     • Constant terms: 3 and -5
     • x terms: -2x and 4x
     • x^2 terms: 2x^2 and 3x^2

2. Combine Like Terms:

   • Add or subtract the coefficients of the like terms.
   • Constant terms: 3 - 5 = -2
   • x terms: -2x + 4x = 2x
   • x^2 terms: 2x^2 + 3x^2 = 5x^2

3. Write the Simplified Expression:

   • Arrange the terms in descending order of their exponents.
   • The simplified expression is 5x^2 + 2x - 2.

Explanation

The process of simplifying polynomial expressions involves combining like terms to obtain a more concise and manageable form. By grouping terms with the same variable and exponent, we can easily add or subtract their coefficients, leading to a simpler representation of the original expression.

Conclusion

Simplifying polynomial expressions like (3-2x+2x^2)+(4x-5+3x^2) is a fundamental skill in algebra. By understanding the concept of like terms and the process of combining them, you can effectively simplify complex expressions and make them easier to work with in further mathematical calculations.