Factorize the equation $25 {(2 a - b)}^{2} - 81 b^{2}$

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

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

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

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

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Solution

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

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