Question 56

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

Solution

$$\left(5-\frac{x^2}{3}\right)^3$$ = $$\left(5-\frac{x^2}{3}\right)\left(5-\frac{x^2}{3}\right)^2$$

= $$\left(5-\frac{x^2}{3}\right)\left(25+\frac{x^4}{9}-\frac{10x^2}{3}\right)$$

= $$125+\frac{5x^4}{9}-\frac{50x^2}{3}-\frac{25x^2}{3}-\frac{x^6}{27}+\frac{10x^4}{9}$$

= $$-\frac{x^6}{27}+\frac{15x^4}{9}-\frac{75x^2}{3}+125$$

= $$-\frac{x^6}{27}+\frac{5x^4}{3}-25x^2+125$$

The coefficient of $$x^2$$ in the expansion = -25

Hence, the correct answer is Option A


Create a FREE account and get:

  • Free SSC Study Material - 18000 Questions
  • 230+ SSC previous papers with solutions PDF
  • 100+ SSC Online Tests for Free

cracku

Boost your Prep!

Download App