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

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Solution

$75 (x + y)^{2} - 48 (x - y)^{2} = 3 [25 (x + y)^{2} - 16 (x - y)^{2}] = 3 [{5 (x + y)^{2}} - {4 (x - y)}^{2}] U s i n g a^{2} - b^{2} = (a + b) (a - b) = 3 [5 (x + y) + 4 (x - y)] [5 (x + y) - 4 (x - y)] = 3 [5 x + 5 y + 4 x - 4 y] [5 x + 5 y - 4 x + 4 y] = 3 (9 x + y) (x + 9 y)$

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