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Simplify the expression (x2 - 5x - 3) - (4x2 + 8x - 9).

Mathematics

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To simplify the expression (x2−5x−3)−(4x2+8x−9)(x^2 - 5x - 3) - (4x^2 + 8x - 9), we need to distribute the negative sign to the second polynomial and then combine like terms.

  1. Distribute the negative sign to each term in the second parenthesis.

    (x2−5x−3)−(4x2+8x−9)=x2−5x−3−4x2−8x+9(x^2 - 5x - 3) - (4x^2 + 8x - 9) = x^2 - 5x - 3 - 4x^2 - 8x + 9

  2. Group the like terms together.

    (x2−4x2)+(−5x−8x)+(−3+9)(x^2 - 4x^2) + (-5x - 8x) + (-3 + 9)

  3. Combine the like terms.

    (1−4)x2+(−5−8)x+(−3+9)(1-4)x^2 + (-5-8)x + (-3+9) −3x2−13x+6-3x^2 - 13x + 6

    Comparing this result with the given options:
    A) −3x2−13x+6-3x^2 - 13x + 6
    B) −2x2−12x+6-2x^2 - 12x + 6
    C) 3x2+13x+63x^2 + 13x + 6
    D) 2x2+12x+62x^2 + 12x + 6

    The simplified expression matches option A.

    The final answer is \boxed{\text{A) -3x^2 - 13x + 6}}.

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