\( x ^ { 2 } + 2 x y - y ^ { 2 } ; \quad \left. \begin{array} { l } { x = 3 } \\ { y = 1 } \end{array} \right. \)

Plugging in \( x = 3 \) and \( y = 1 \) into the expression \( x^2 + 2xy - y^2 \), we get: \[ 3^2 + 2(3)(1) - 1^2 = 9 + 6 - 1 = 14. \] So, the expression evaluates to 14! In tackling similar mathematical expressions, always remember to substitute the variables carefully and perform operations step by step. A common mistake is to rush through calculations or misinterpret the order of operations, which can lead to incorrect results. Take your time and double-check each step!