What is the coefficient of x^{2} in the expansion of (5-\frac{x^{2}}{3})^{3} ?

SSC CGL 24 Aug 2021 Shift 3 Paper

Question : 56 of 100

Marks: +1, -0

What is the coefficient of

x^{2}

in the expansion of

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

Solution:

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

=125-\;{x^{6}}/{27}-3 × 5 × \;{x^{2}}/{3}(5-\;{x^{2}}/{3})

[ ∵ (a-b)^{3}=a^{3}-b^{3}-3 a b(a-b)]

=125-\;{x^{6}}/{27}-3 × 5 × \;{x^{2}}/{3}\;× 5-3

\;× 5 × \;{x^{2}}/{3} × \;{x^{2}}/{3}

=125-\;{x^{6}}/{27}-25 x^{2}-\;{5}/{3} x^{4}

The coefficient of

x^{2}

-25

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