Factorize $2 (2 x - 5 y) (3 x + 4 y) - 6 (2 x - 5 y) (x - y)$ by taking out the common factors

14 y (2 x - 5 y)

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4 y (2 x - 5 y)

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13 y (2 x - y)

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19 y (x - 3 y)

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Solution

The correct option is A $14 y (2 x - 5 y)$
$2 (2 x - 5 y) (3 x + 4 y) - 6 (2 x - 5 y) (x - y)$
$= 2 (2 x - 5 y) [(3 x + 4 y) - 3 (x - y)]$
$= 2 (2 x - 5 y) (3 x + 4 y - 3 x + 3 y)$

$= 14 y (2 x - 5 y)$

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