17. Expand and simplify \( (\sqrt{7}-\sqrt{ } 3)^{2} \)

To expand and simplify \( (\sqrt{7}-\sqrt{3})^{2} \), we use the formula for the square of a binomial, which states \( (a - b)^{2} = a^{2} - 2ab + b^{2} \). Here, \( a = \sqrt{7} \) and \( b = \sqrt{3} \). So, \[ (\sqrt{7}-\sqrt{3})^{2} = (\sqrt{7})^{2} - 2(\sqrt{7})(\sqrt{3}) + (\sqrt{3})^{2} \] Calculating each term: - \( (\sqrt{7})^{2} = 7 \) - \( 2(\sqrt{7})(\sqrt{3}) = 2\sqrt{21} \) - \( (\sqrt{3})^{2} = 3 \) Now combine all terms: \[ 7 - 2\sqrt{21} + 3 = 10 - 2\sqrt{21} \] So, the final simplified expression is: \[ 10 - 2\sqrt{21} \]