Question:
Factorize each of the following expression:
x2 − 11xy − x + 11y
Solution:
$x^{2}-11 x y-x+11 y=\left(x^{2}-x\right)+(11 y-11 x y) \quad[$ Regrouping the expressions $]$
$=x(x-1)+11 y(1-x)$
$=x(x-1)-11 y(x-1)$ $[\because(1-x)=-(x-1)]$
$=(x-11 y)(x-1)$ [Taking out the common factor $(x-1)$ ]