Question

Resolve the following quadratic trinomial into factors:

$(x-2y{)}^2-5(x-2y)+6$

Answer 1

Given: $(x-2y{)}^2-5(x-2y)+6$

Let $(x-2y)=a$

$\Rightarrow a^2-5a+6$

On splitting the middle term, we get

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

$=a(a-3)-2(a-3)$

$=(a-3)(a-2)$

$=(x-2y-3)(x-2y-2)$

$\therefore (x-2y{)}^2-5(x-2y)+6=(x-2y-3\left)\right(x-2y-2)$