What is the coefficient of $$x^2$$ in the expansion of $$\left(5-\frac{x^2}{3}\right)^3$$?
$$\left(5-\frac{x^2}{3}\right)^3$$ =Â $$\left(5-\frac{x^2}{3}\right)\left(5-\frac{x^2}{3}\right)^2$$
=Â $$\left(5-\frac{x^2}{3}\right)\left(25+\frac{x^4}{9}-\frac{10x^2}{3}\right)$$
=Â $$125+\frac{5x^4}{9}-\frac{50x^2}{3}-\frac{25x^2}{3}-\frac{x^6}{27}+\frac{10x^4}{9}$$
=Â $$-\frac{x^6}{27}+\frac{15x^4}{9}-\frac{75x^2}{3}+125$$
=Â $$-\frac{x^6}{27}+\frac{5x^4}{3}-25x^2+125$$
The coefficient of $$x^2$$ in the expansion = -25
Hence, the correct answer is Option A
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