Factorize :
$5 a^{2} - b^{2} - 4 a b + 7 a - 7 b$

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

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(a + b) (5 a + b + 7)

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

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none of the above

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Solution

The correct option is C $(a - b) (5 a + b + 7)$
$5 a^{2} - b^{2} - 4 a b + 7 a - 7 b$
$= 4 a^{2} + a^{2} - b^{2} - 4 a b + 7 a - 7 b$
$= (a^{2} - b^{2}) + (4 a^{2} - 4 a b) + (7 a - 7 b)$
$= (a + b) (a - b) + 4 a (a - b) + 7 (a - b)$
$= (a - b) (5 a + b + 7)$

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