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

-25

(a - b)³ = a³ - b³ - 3ab(a-b)

= $\left(5-\frac{x^2}{3}\right)^3$ = 5³ - ($\frac{x^2}{3}$)³ - 3(5)($\frac{x^2}{3}$)$\left(5-\frac{x^2}{3}\right)^3$

= 125 - \(\frac{x^6}{27}\) - \(\frac{15x^2}{3}\)($\left(5-\frac{x^2}{3}\right)$)

= 125 - \(\frac{x^6}{27}\) - 25x² + \(\frac{5x^4}{3}\) 

So we can see that the coefficient of x² in the expension is -25