Factorize: $5 - (3 a^{2} - 2 a) (6 - 3 a^{2} + 2 a)$

(a - 4) (a + 3) (3 a + 4) (3 a - 5)

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(2 a - 1) (2 a + 1) (3 a + 1) (3 a - 5)

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(a - 1) (a + 1) (a + 3) (3 a - 5)

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(a - 1) (a + 1) (3 a + 1) (3 a - 5)

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Solution

The correct option is D $(a - 1) (a + 1) (3 a + 1) (3 a - 5)$
$\Rightarrow 5 - (3 a^{2} - 2 a) (6 - 3 a^{2} + 2 a)$
$\Rightarrow 5 - (3 a^{2} - 2 a) [6 - (3 a^{2} - 2 a)]$
Let $(3 a^{2} - 2 a) = x$
$\Rightarrow 5 - x (6 - x)$
$\Rightarrow 5 - 6 x + x^{2}$
$\Rightarrow x^{2} - 6 x + 5$
$\Rightarrow x^{2} - x - 5 x + 5$
$\Rightarrow x (x - 1) - 5 (x - 1)$
$\Rightarrow (x - 1) (x - 5)$
$Substituting x = (3 a^{2} - 2 a)$
$\Rightarrow [3 a^{2} - 2 a - 1] [3 a^{2} - 2 a - 5]$
$\Rightarrow [3 a^{2} - 3 a + a - 1] [3 a^{2} + 3 a - 5 a - 5]$
$\Rightarrow [3 a (a - 1) + 1 (a - 1)] [3 a (a + 1) - 5 (a + 1)]$
$\Rightarrow [(a - 1) (3 a + 1)] [(a + 1) (3 a - 5)]$
$\Rightarrow (a - 1) (a + 1) (3 a + 1) (3 a - 5)$

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