\[\boxed{\text{1000.}\text{\ }еуроки - ответы\ на\ пятёрку}\]
\[\textbf{а)}\ (n + 1)^{2} - (n - 1)^{2} = n^{2} +\]
\[+ 2n + 1 - n^{2} + 2n - 1 =\]
\[= 4n \Longrightarrow делится\ на\ 4.\]
\[\textbf{б)}\ (2n + 3)^{2} - (2n - 1)^{2} =\]
\[= 4n^{2} + 12n + 9 - 4n^{2} +\]
\[+ 4n - 1 = 16n + 9 =\]
\[= 8 \cdot (2n + 1) \Longrightarrow делится\ на\ 8.\]
\[\textbf{в)}\ (3n + 1)^{2} - (3n - 1)^{2} =\]
\[= 9n^{2} + 6n + 1 - 9n^{2} +\]
\[+ 6n - 1 =\]
\[= 12n \Longrightarrow делится\ на\ 12.\]
\[\textbf{г)}\ (5n + 1)^{2} - (2n - 1)^{2} =\]
\[= 25n^{2} + 10n + 1 - 4n^{2} +\]
\[+ 4n - 1 = 21n^{2} + 14n =\]
\[= 7n(3n + 2) \Longrightarrow делится\ на\ 7.\]