Show that ${(3 x + 7)}^{2} - 84 x = {(3 x - 7)}^{2}$

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Solution

$(3 x + 7)^{2} - 84 x = (3 x - 7)^{2}$
$\Rightarrow$ $L . H . S . = (3 x + 7)^{2} - 84 x$
$= (3 x)^{2} + 2 (3 x) (7) + (7)^{2} - 84 x$
$= 9 x^{2} + 42 x + 49 - 84 x$
$= 9 x^{2} - 42 x + 49$
$= (3 x - 7)^{2}$
$∴$ $L . H . S = R . H S .$
$∴$ $(3 x + 7)^{2} - 84 x = (3 x - 7)^{2}$ ---- [ Hence proved ]

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