Show that:
${(a + b)}^{2} - {(a - b)}^{2} = 4 a b$

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Solution

$L H S = (a + b)^{2} - (a - b)^{2}$
$= a^{2} + b^{2} + 2 a b - (a^{2} + b^{2} - 2 a b)$
$= a^{2} + b^{2} + 2 a b - a^{2} - b^{2} + 2 a b$
$= 4 a b$
$= R H S$

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