2) If \( x-y=3, x+y=7 \), then \( x^{2}-y^{2}=\ldots \) \( (21,10,4,9) \)

To solve the equations \( x - y = 3 \) and \( x + y = 7 \), we can first add these two equations together. This gives us \( (x - y) + (x + y) = 3 + 7 \), simplifying to \( 2x = 10 \), leading to \( x = 5 \). Now, we substitute \( x \) back into the first equation: \( 5 - y = 3 \), which yields \( y = 2 \). Now, to find \( x^2 - y^2 \), we use the difference of squares formula: \( x^2 - y^2 = (x - y)(x + y) \). We already have \( x - y = 3 \) and \( x + y = 7 \). So, \( x^2 - y^2 = 3 \cdot 7 = 21 \). The final answer is 21!