Anonymous
Anonymous asked in Science & MathematicsMathematics · 9 years ago

In binomial theorem: how do I find k?

In regards to finding the coefficient of x^18 when expanding the term (½x² - 5) ^16

how do I find k? I understand the how to find the coefficient, but without k I am a little lost.

1 Answer

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  • Anonymous
    9 years ago
    Favorite Answer

    First just look at your terms inside the bracket.

    There is an x^2 term and an x^0 term all exponentiated by 16.

    (x^2)^9 = 18

    Therefore you are looking for the term that involves (1/2 x^2)^9 and (-5)^7

    Using the binomial theorem, you find that the coefficient is:

    16 choose 7

    = 16! / 7!9!

    So the total coefficient of x^18 is:

    = 11440 * (1/2 x^2)^9 * (-5)^7

    = -11440 * 1/512 x^18 * (5)^7

    = -893,750,000 * 1/512 x^18

    = -55,859,375 / 32 x^18

    Coefficient = -55,859,375 / 32

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