x^3/64 - 64/x^3 – InterviewSolution

1.

x^3/64 - 64/x^3

Answer»

x^3/64 - 64/x^3

= (x/4)^3 - (4/x)^3

Using identitya^3 – b^3 = (a – b) (a^2 + ab + b^2).

= (x/4 - 4/x)(x^2/16 + x/4*4/x + 16/x^2)

= (x/4 - 4/x)(x^2/16 + 1 + 16/x^2)

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