Evaluate : ( a 2 ~b + 2 ~b a ) ( a 2 ~b - 2 ~b a ) - Vidyadip

Question

Evaluate : $\left(\frac{\mathrm{a}}{2 \mathrm{~b}}+\frac{2 \mathrm{~b}}{\mathrm{a}}\right)\left(\frac{\mathrm{a}}{2 \mathrm{~b}}-\frac{2 \mathrm{~b}}{\mathrm{a}}\right)$

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Answer

$ \left(\frac{\mathrm{a}}{2 \mathrm{~b}}+\frac{2 \mathrm{~b}}{\mathrm{a}}\right)\left(\frac{\mathrm{a}}{2 \mathrm{~b}}-\frac{2 \mathrm{~b}}{\mathrm{a}}\right)$
$ =\frac{\mathrm{a}}{2 \mathrm{~b}}\left(\frac{\mathrm{a}}{2 \mathrm{~b}}+\frac{2 \mathrm{~b}}{\mathrm{a}}\right)+\frac{2 \mathrm{~b}}{\mathrm{a}}\left(\frac{\mathrm{a}}{2 \mathrm{~b}}-\frac{2 \mathrm{~b}}{\mathrm{a}}\right)$
$ =\frac{\mathrm{a}^2}{4 \mathrm{~b}^2}-1+1-\frac{4 \mathrm{~b}^2}{\mathrm{a}^2}$
$ =\frac{\mathrm{a}^2}{4 \mathrm{~b}^2}-\frac{4 \mathrm{~b}^2}{\mathrm{a}^2}$

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