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Calculus

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Find the constant term in the expansion of [x + (3/x squared)]^9

Find the coefficient of (x)^4(y)^9 in the expansion of (x + (2)(y)^3)^7

  • Calculus - ,

    for the first one, first of all, find the general term.
    I got
    C(7,r)x^(7-r)(3/x^2)^r
    =c(7,r)(3)^r x^(9-3r)

    for that to be a constant the exponent of the x terms must be zero,so
    9-3r=0
    r=3

    so the constant term is C(7,3)(3^3) = 2268

    for the second question, to have the x^4, it must be term number 3.
    You work this one out, let me know what you got

  • Calculus - ,

    correction, whenever you see a 7, it should be a 9

    so here it is again
    for the first one, first of all, find the general term.
    I got
    C(9,r)x^(9-r)(3/x^2)^r
    =c(9,r)(3)^r x^(9-3r)

    for that to be a constant the exponent of the x terms must be zero,so
    9-3r=0
    r=3

    so the constant term is C(9,3)(3^3) = 2268

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