Lets Factorize the given expression:-
[tex]️{x}^{2} + 4xy - 117 {y}^{2} [/tex]
Splitting the middle term :-
[tex]{x}^{2} - 9xy + 13xy - 117 {y}^{2} [/tex]
[tex]( {x}^{2} - 9xy) + (13xy - 117 {y}^{2})[/tex]
[tex]x(x - 9y) + 13y(x - 9y)[/tex]
[tex](x - 9y)(x + 13y)[/tex]
So, the final answer is:-
[tex](x - 9y)(x + 13y)[/tex]
