Question 439938
Key things to notice are;
(1) 
The fact that the signs have the pattern {{{ ax^2 - b*x*y - c*y^2 }}}
tells me that the factors will look like {{{(x + y)*(x - y)}}} (with coefficients)
and that the {{{ -x*y }}} of the factoring will be greater than the {{{ +x*y }}}
to give me the {{{ -b*x*y }}} middle term of the equation.
(2)
The fact that {{{ 77 = 7*11 }}} and {{{ 11 - 7 = 4 }}} tells me where the
{{{-4}}} in the middle term comes from.
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With these observations, I can try to factor it:
{{{ x^2 - 4x*y - 77y^2 = ( x + 7y )*( x - 11y ) }}} 
Notice the {{{11}}} has to have the (-) sign, and
the difference of {{{11}}} and {{{7}}} has to be {{{4}}}