Factorize :
$(a^{2} - 3 a) (a^{2} - 3 a + 7) + 10$

(a^{2} - 3 a - 5) (2 a - 2) (a + 1)

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(a^{2} - 3 a + 5) (a - 2) (a + 1)

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(a^{2} + 3 a - 5) (2 a - 2) (a - 1)

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(a^{2} - 3 a + 5) (a - 2) (a - 1)

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Solution

The correct option is D $(a^{2} - 3 a + 5) (a - 2) (a - 1)$
$(a^{2} - 3 a) (a^{2} - 3 a + 7) + 10$
$= (a^{2} - 3 a)^{2} + 7 (a^{2} - 3 a) + 10$
$= (a^{2} - 3 a)^{2} + 5 (a^{2} - 3 a) + 2 (a^{2} - 3 a) + 10$
$= (a^{2} - 3 a) ((a^{2} - 3 a) + 5) + 2 ((a^{2} - 3 a) + 5)$
$= ((a^{2} - 3 a) + 5) (a^{2} - 3 a + 2)$
$= (a^{2} - 3 a + 5) (a^{2} - 2 a - a + 2)$
$= (a^{2} - 3 a + 5) (a (a - 2) - 1 (a - 2))$
$= (a^{2} - 3 a + 5) (a - 2) (a - 1)$

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Similar questions

Simplify:-

1. (a^{2 _}3a + 7) × (2a + 3)

\frac{a - b}{a} + \frac{1}{2} (\frac{a - b}{a})^{2} + \frac{1}{3} (\frac{a - b}{a})^{3} + = \dots

\frac{(a - b)}{a} + \frac{1}{2} (\frac{a - b}{a})^{2} + \frac{1}{3} (\frac{a - b}{a})^{3} + . . . . .

7 + 2 (a + 1) - 3 a = 5 a

a^{2} - 2 a + {5 a^{2} - (3 a - 4 a^{2})}

10 a^{2} - 5 a

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