Simplify the given expression. (x-\frac{2}{x})^{3}-(x+\frac{2}{x})^{3}

Correct Answer is : −4(3x+4x3)

SSC CHSL 10 Aug 2021 Shift 1 Paper

Section: Quantitative Aptitude

Question : 54 of 100

Marks: +1, -0

Simplify the given expression.

(x-\;{2}/{x})^{3}-(x+\;{2}/{x})^{3}

Solution:

Given,

(x-\;{2}/{x})^{3}-(x+\;{2}/{x})^{3}

=[x^{3}-(\;{2}/{x})^{3}-3 × x × \;{2}/{x} ×(x-\;{2}/{x})]

-[x^{3}+(\;{2}/{x})^{3}+3 × x × \;{2}/{x} ×(x+\;{2}/{x})]

=x^{3}-\;{8}/{x^{3}}-6(x-\;{2}/{x})-x^{3}-\;{8}/{x^{3}}

=-\;{16}/{x^{3}}-6 x+\;{12}/{x}-6 x-\;{12}/{x}

=-\;{16}/{x^{3}}-12 x=-4(3 x+\;{4}/{x^{3}})

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