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(i) $(5 a-3 b)^{3}=(5 a)^{3}-(3 b)^{3}-3(5 a)^{2}(3 b)+3(5 a)(3 b)^{2}$

$=125 a^{3}-27 b^{3}-225 a^{2} b+135 a b^{2}$

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

$=27 x^{3}-\frac{125}{x^{3}}-135 x+\frac{225}{x}$

(iii) $\left(\frac{4}{5} a-2\right)^{3}=\left(\frac{4}{5} a\right)^{3}-(2)^{3}-3\left(\frac{4}{5} a\right)^{2}(2)+3\left(\frac{4}{5} a\right)(2)^{2}$

$=\frac{64}{125} a^{3}-8-\frac{96}{25} a^{2}+\frac{48}{5} a$