(3x^2+4x-1)+(-2x^2-3x+2)

Jasonbradley

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Jun 16, 2024

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Simplifying Polynomial Expressions: (3x^2 + 4x - 1) + (-2x^2 - 3x + 2)

This article will guide you through simplifying the polynomial expression: (3x^2 + 4x - 1) + (-2x^2 - 3x + 2).

Understanding the Expression

The given expression involves two polynomials being added together. A polynomial is an expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication.

The terms within each polynomial are separated by either a plus (+) or minus (-) sign.

Simplifying the Expression

To simplify the expression, we need to combine like terms. Like terms are terms that have the same variable raised to the same power.

1. Identify like terms:

   • x² terms: 3x² and -2x²
   • x terms: 4x and -3x
   • Constant terms: -1 and 2

2. Combine like terms:

   • 3x² + (-2x²) = x²
   • 4x + (-3x) = x
   • -1 + 2 = 1

3. Write the simplified expression: The simplified expression is x² + x + 1.

Explanation

We combined the coefficients of the like terms while keeping the variables and their exponents unchanged. This process results in a simplified expression with fewer terms, making it easier to understand and work with.

Conclusion

Simplifying polynomial expressions involves combining like terms. By following the steps outlined above, we were able to simplify the given expression to x² + x + 1. This process is fundamental in various areas of mathematics, including algebra and calculus.