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Question
Expand `(2x^2 - 3/x)^3`
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Solution
`(2x^2 - 3/x)^3 = ""^3"C"_0 (2x^2)^3 + ""^3"C"_1 (2x^2)^2 (- 3/x) + ""^3"C"_2 (2x^2)^1 (- 3/x)^2 + ""^3"C"_3 (- 3/x)^3`
3C0 = 3C3 = 1 ; 3C1 = 3C2 = 3
= `1(8)(x^6) + 3(4x^4) (-3/x) + 3(2x^2) (9/x^2) + 1(- 27/x^3)`
= `8x^6 - (36x^4)/x + (54x^2)/x^2 - 27/x^3`
= `8x^6 - 36x^3 + 54 - 27/x^3`
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