Answer
$(n+1)^{2}$
Work Step by Step
$\frac{((n+1)!)^{2}}{((n)!)^{2}}=\frac{1^{2}\times2^{2}\times...\times(n-1)^{2}\times n^{2}\times(n+1)^{2}}{1^{2}\times2^{2}\times...\times(n-1)^{2}\times n^{2}}$
$=(n+1)^{2}$
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