Factorize: $(3 x - 2 y)^{2} + 3 (3 x - 2 y) - 10$

(3 x + 2 y - 5) (3 x - 2 y + 2)

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(3 x - 2 y + 5) (3 x - 2 y - 2)

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(3 x + 2 y + 5) (3 x + 2 y - 2)

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(3 x - 2 y - 5) (3 x - 2 y - 2)

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Solution

The correct option is B $(3 x - 2 y + 5) (3 x - 2 y - 2)$
$\Rightarrow (3 x - 2 y)^{2} + 3 (3 x - 2 y) - 10$
Let $(3 x - 2 y) = a$
$\Rightarrow a^{2} + 3 a - 10$
$\Rightarrow a^{2} + 5 a - 2 a - 10$
$\Rightarrow a (a + 5) - 2 (a + 5)$
$\Rightarrow (a + 5) (a - 2)$
$Substituting a = (3 x - 2 y)$
$\Rightarrow (3 x - 2 y + 5) (3 x - 2 y - 2)$

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