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Find the coefficient of the x^2 term in the expansion of (3x - (2/x^2))^8

  • Calculus -

    I would advice to take out the 1/x^2 term first:

    (3x - (2/x^2))^8 =

    1/x^16 (3 x^3 - 2)^8 =

    So you need to get x^18 from the expansion of the bracket:

    (3 x^3 - 2)^8 contains a term:

    (3 x^3)^6 (-2)^2 Binomial(8,6)

    So, the coefficient is 81648.

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