Evaluate $75 (x + y)^{2} - 48 (x - y)^{2}$

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Solution

$75 (x + y)^{2} - 48 (x - y)^{2}$
$= 75 (x^{2} + y^{2} + 2 x y) - 48 (x^{2} + y^{2} - 2 x y)$
$= 75 x^{2} + 75 y^{2} + 150 x y - 48 x^{2} - 48 y^{2} + 96 x y$
$= 27 x^{2} + 27 y^{2} + 246 x y$

This is the required solution.

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