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March 26, 2017

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write expansions:

1) (4/3x+3/4y)^3

  • maths - ,

    in general
    (a+b)^3 = a^3 + 3a^2 b + 3a b^2 + b^3

    then ...
    (4/3x+3/4y)^3
    = (4/3)^3 x^3 + 3(4/3)^2 x^2 (3/4)y + 3(4/3)x (3/4)^2 y^2 + (3/4)^3 y^3
    = 64x^3/27 + 144x^2 y/36 + 108xy^2/48 + 27y^3/64
    = 64x^3/27 + 4x^2y + 9xy^2/4 + 27y^3/64

    testing by letting x=1, y=1
    (4/3 + 3/4)^3 = appr 9.0422..
    my expression at the end = .0422..

    I assume you meant it the way you typed it
    if you meant
    ( 4/(3x) + 3/(4x) )^3 it would totally change the answer.

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