Show that :
${(9 l m - 3 n)}^{2} - {(9 l m + 3 n)}^{2} = - 108 l m n$

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Solution

$L . H . S = {(9 l m - 3 n)}^{2} - {(9 l m + 3 n)}^{2}$

$= (9 l m - 3 n - 9 l m - 3 n) (9 l m - 3 n + 9 l m + 3 n)$

$= - 6 n \times 18 l m$

$= - 108 l m n$

$= R . H . S$

Hence proved.

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