Factor the expression. \[ x^{2}+19 x y-92 y^{2} \] \( x^{2}+19 x y-92 y^{2}=\square \) (Type your answer in factored form.)

To factor the expression \( x^{2}+19xy-92y^{2} \), we need to find two numbers that multiply to \(-92y^{2}\) (the product of the coefficient of \(x^{2}\) and the constant term) and add to \(19y\) (the coefficient of \(xy\)). The numbers that satisfy these conditions are \(23y\) and \(-4y\). We can rewrite the expression using these two numbers: \[ x^{2} + 23xy - 4xy - 92y^{2} \] Now, we can group the terms: \[ (x^{2} + 23xy) + (-4xy - 92y^{2}) \] Factoring out \(x\) from the first group and \(-4y\) from the second group gives us: \[ x(x + 23y) - 4y(x + 23y) \] Next, we can factor out the common term \((x + 23y)\): \[ (x + 23y)(x - 4y) \] Thus, the factored form of the expression \( x^{2}+19xy-92y^{2} \) is: \[ (x + 23y)(x - 4y) \]