Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

1. Expand (x + 1)(x − 2)(x + 3)?

PreCalc

4 Answers

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  • 2 months ago

    First expand one pair of binomials (I chose x+1 and x-2):

    (x² -2x + x - 2)(x + 3)

    Combine like terms:

    = (x² - x - 2)(x + 3)

    We can now expand the multiplication. First multiply that new trinomial by x and then by 3:

    x(x² - x - 2) + 3(x² - x - 2)

    Distribute:

    = x^3 - x² - 2x + 3x² - 3x - 6

    Combine like terms:

    x^3 + (-x² + 3x²) + (-2x - 3x) - 6

    = x^3 + 2x² - 5x - 6

    Answer:

    x^3 + 2x² - 5x - 6

  • 2 months ago

    (x + 1)(x − 2)(x + 3)

    = (x^2 − x − 2)(x + 3)

    = x^3 + 2x^2 − 5x − 6

  • 2 months ago

    (x+1)(x - 2) = x^2 - x - 2.

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

    = x^3 - x^2 + 3x^2 - 2x - 3x - 6

    = x^3 + 2x^2 - 5x - 6

  • 2 months ago

    (x + 1)(x − 2)(x + 3)

    (x + 1)(x + 3) = x² + 4x + 3

    so we have

    (x − 2)(x² + 4x + 3)

    x(x² + 4x + 3) – 2(x² + 4x + 3)

    x³ + 4x² + 3x – 2x² – 8x – 6

    x³ + 2x² – 5x – 6

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