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

(a) (a + 1) (a - 1) (a + 1)

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

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

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

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Solution

The correct option is C $(3 a - 5) (a + 1) (a - 1) (3 a + 1)$
$5 - (3 a^{2} - 2 a) (6 - 3 a^{2} + 2 a)$
$= 5 - 6 (3 a^{2} - 2 a) + (3 a^{2} - 2 a)^{2}$
$= [(3 a^{2} - 2 a)^{2} - 5 (3 a^{2} - 2 a)] - [(3 a^{2} - 2 a) - 5]$
$= (3 a^{2} - 2 a) (3 a^{2} - 2 a - 5) - 1 (3 a^{2} - 2 a - 5)$
$= (3 a^{2} - 2 a - 5) (3 a^{2} - 2 a - 1)$
$= (3 a^{2} - 5 a + 3 a - 5) (3 a^{2} - 3 a + a - 1)$
$= [3 a (a + 1) - 5 (a + 1)] [3 a (a - 1) + (a - 1)]$
$= (a + 1) (3 a - 5) (a - 1) (3 a + 1)$

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