$25 (x + y)^{2} - 4 (x - y)^{2}$ is equal to

21 x^{2}

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(3 x - 7 y) (7 x + 3 y)

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25 x^{2} + 29 y^{2}

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(7 x + 3 y) (3 x + 7 y)

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Solution

The correct option is D $(7 x + 3 y) (3 x + 7 y)$
$25 (x + y)^{2} - 4 (x - y)^{2} = [5 (x + y)^{2} - [2 (x - y)]^{2} = (5 x + 5 y)^{2} - (2 x - y)^{2}$
$= (5 x + 5 y + 2 x - 2 y) (5 x + 5 y - 2 x + 2 y)$
$= (7 x + 3 y) (3 x + 7 y)$

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