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(3x^2+2x-5)-(5x^2-4x+1)

2 min read Jun 16, 2024
(3x^2+2x-5)-(5x^2-4x+1)

Simplifying Polynomial Expressions: (3x^2 + 2x - 5) - (5x^2 - 4x + 1)

This article will guide you through the process of simplifying the polynomial expression: (3x^2 + 2x - 5) - (5x^2 - 4x + 1).

Understanding the Expression

The expression involves subtracting two trinomials. Remember that trinomials are polynomials with three terms.

The Steps to Simplification

  1. Distribute the negative sign: The minus sign in front of the second parenthesis means we multiply each term inside the parenthesis by -1.

    (3x^2 + 2x - 5) + (-1 * 5x^2) + (-1 * -4x) + (-1 * 1)

  2. Simplify: This simplifies to:

    3x^2 + 2x - 5 - 5x^2 + 4x - 1

  3. Combine like terms: Combine the x^2 terms, the x terms, and the constant terms.

    (3x^2 - 5x^2) + (2x + 4x) + (-5 - 1)

  4. Final result:

    -2x^2 + 6x - 6

Conclusion

Therefore, the simplified form of the expression (3x^2 + 2x - 5) - (5x^2 - 4x + 1) is -2x^2 + 6x - 6.

This process of simplifying polynomial expressions is crucial in algebra and helps us manipulate equations and solve for unknown variables.

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