Question

Factorize by splitting the middle term :

$9(x-2y{)}^2-4(x-2y)-13$

Answer 1

$9(x-2y{)}^2-4(x-2y)-13$

$=9a^2-4a-13$, where $a=x-2y$

$=9a^2-13a+9a-13$

$=a(9a-13)+(9a-13)$

$=(9a-13)(a+1)$

$=(x-2y+1)\left[9\right(x-2y)-13]$

$=(x-2y+1)(9x-18y-13)$