Expand:
$[\frac{2}{3} x - \frac{3}{2 x} + 1]^{2}$

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Solution

$\begin{matrix} W e h a v e {[\frac{2 x}{3} - \frac{3}{2 x} + 1]}^{2} = {[(\frac{2 x}{2}) + (- \frac{3}{2 x}) + (1)]}^{2} = {(\frac{2 x}{2})}^{2} + {(- \frac{3}{2 x})}^{2} + {(1)}^{2} + 2 (\frac{2 x}{2}) (- \frac{3}{2 x}) + 2 (- \frac{3}{2 x}) (1) + 2 (1) (\frac{2 x}{2}) u sin g f o r m u l a {[a + b + c]}^{2} = a^{2} + b^{2} + c^{2} + 2 a c + 2 b c + 2 c a = \frac{4 x^{2}}{2} + \frac{9}{4 x^{2}} + 1 - \frac{3}{2} - \frac{3}{x} + 2 x = \frac{4 x^{2}}{2} + \frac{9}{4 x^{2}} + 2 x - \frac{3}{x} - \frac{1}{2} . I t i s i t^{'} s a n e d f r o m . \end{matrix}$

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