Answer 1

\[x^2 - 11xy - x + 11y = ( x^2 - x) + (11y - 11xy) \][Regrouping the expressions]
\[ = x(x - 1) + 11y(1 - x)\]
\[ = x(x - 1) - 11y(x - 1) [ \because (1 - x) = - (x - 1)]\]
\[ = (x - 11y)(x - 1) \][Taking out the common factor (x - 1)]