Question

Factories the following
$(a^2-a{)}^2-8(a^2-a)+12$

Answer 1

Given:

$(a^2-a{)}^2-8(a^2-a)+12$

Let $a^2-a=y.....\left(1\right)$

Then $y^2-8y+12$

$\Rightarrow y^2-6y-2y+12$

$\Rightarrow (y-2)(y-6)$

Therefore,

$(a^2-a-2)(a^2-a-6)$ [From (1)]

Or we can write-

$(a^2-2a+a-2)(a^2-3a+2a-6)$

$\Rightarrow (a+1)(a-2)(a-3)(a+2)$