Factorize:
$25 (2 a - b)^{2} - 81 b^{2}$ .

4 (5 a + 2 b) (5 a - 7 b)

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3 (5 a + 2 b) (5 a - 7 b)

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5 (5 a + 2 b) (5 a - 7 b)

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(5 a + 2 b) (5 a - 7 b)

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Solution

The correct option is A $4 (5 a + 2 b) (5 a - 7 b)$
$25 (2 a - b)^{2} - 81 b^{2}$
$= (10 a - 5 b)^{2} - (9 b)^{2}$
Using [ $a^{2} - b^{2} = (a + b) (a - b)$ ], we get
$= (10 a - 5 b + 9 b) (10 a - 5 b - 9 b)$
$= (10 a + 4 b) (10 a - 14 b)$
$= 4 (5 a + 2 b) (5 a - 7 b)$

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