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

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

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

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

Understanding the Steps

  1. Distribute the negative sign: The minus sign before the second parenthesis means we multiply each term inside the parenthesis by -1.
  2. Combine like terms: Identify terms with the same variable and exponent and add or subtract their coefficients.

Step-by-Step Solution

  1. Distribute the negative sign:

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

    Simplifying:

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

  2. Combine like terms:

    x^2 terms: 2x^2 - 3x^2 = -x^2 x terms: -2x - 4x = -6x Constant terms: 3 + 5 = 8

  3. Final expression:

    -x^2 - 6x + 8

Conclusion

Therefore, the simplified form of the expression (3-2x+2x^2)-(4x-5+3x^2) is -x^2 - 6x + 8.

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