Expand the following: (4-1 3 x )^3 - Vidyadip

Question

Expand the following:
$\Big(4-\frac{1}{3{\text{x}}}\Big)^3$

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Answer

$\Big(4-\frac{1}{3{\text{x}}}\Big)^3=(4)^3+\Big(-\frac{1}{3\text{x}}\Big)^3+ 3(4)\Big(-\frac{1}{3\text{x}}\Big)\Big(4-\frac{1}{3{\text{x}}}\Big)$
[Using identity, $\left.(a-b)^3=a^3-b^3+3 a(-b)(a-b)\right]$
$= 64 - \frac{1}{27\text{x}^3}-\frac{4}{\text{x}}\Big(4-\frac{1}{3\text{x}}\Big)$
$= 64 - \frac{1}{27\text{x}^3}-\frac{16}{\text{x}}+\frac{4}{3\text{x}^2}$

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