ANSWER
The fully factored form is
[tex](x - 6y)(x - 4y)[/tex]
EXPLANATION
The given expression is
[tex] {x}^{2} - 10xy + 24 {y}^{2} [/tex]
We need to split the middle term to obtain
[tex] {x}^{2} - 4xy - 6xy + 24 {y}^{2} [/tex]
We factor to obtain,
[tex]x(x - 4y) - 6y(x -4 y)[/tex]
We factor further to obtain,
[tex](x - 6y)(x - 4y)[/tex]
