展開する (n^2+n+5)^{10}

解

展開する

(n^{2} + n + 5)^{10}

n^{20} + 10 n^{19} + 95 n^{18} + 570 n^{17} + 3135 n^{16} + 13452 n^{15} + 53010 n^{14} + 174420 n^{13} + 529245 n^{12} + 1377310 n^{11} + 3313201 n^{10} + 6886550 n^{9} + 13231125 n^{8} + 21802500 n^{7} + 33131250 n^{6} + 42037500 n^{5} + 48984375 n^{4} + 44531250 n^{3} + 37109375 n^{2} + 19531250 n + 9765625

解答ステップ

(n^{2} + n + 5)^{10}

(n^{2} + n + 5)^{10} = (n^{2} + n + 5) (n^{2} + n + 5) (n^{2} + n + 5) (n^{2} + n + 5) (n^{2} + n + 5) (n^{2} + n + 5) (n^{2} + n + 5) (n^{2} + n + 5) (n^{2} + n + 5) (n^{2} + n + 5)

= (n^{2} + n + 5) (n^{2} + n + 5) (n^{2} + n + 5) (n^{2} + n + 5) (n^{2} + n + 5) (n^{2} + n + 5) (n^{2} + n + 5) (n^{2} + n + 5) (n^{2} + n + 5) (n^{2} + n + 5)

拡張

(n^{2} + n + 5) (n^{2} + n + 5) (n^{2} + n + 5) (n^{2} + n + 5) (n^{2} + n + 5) (n^{2} + n + 5) (n^{2} + n + 5) (n^{2} + n + 5) (n^{2} + n + 5) (n^{2} + n + 5) : n^{20} + 10 n^{19} + 95 n^{18} + 570 n^{17} + 3135 n^{16} + 13452 n^{15} + 53010 n^{14} + 174420 n^{13} + 529245 n^{12} + 1377310 n^{11} + 3313201 n^{10} + 6886550 n^{9} + 13231125 n^{8} + 21802500 n^{7} + 33131250 n^{6} + 42037500 n^{5} + 48984375 n^{4} + 44531250 n^{3} + 37109375 n^{2} + 19531250 n + 9765625

= n^{20} + 10 n^{19} + 95 n^{18} + 570 n^{17} + 3135 n^{16} + 13452 n^{15} + 53010 n^{14} + 174420 n^{13} + 529245 n^{12} + 1377310 n^{11} + 3313201 n^{10} + 6886550 n^{9} + 13231125 n^{8} + 21802500 n^{7} + 33131250 n^{6} + 42037500 n^{5} + 48984375 n^{4} + 44531250 n^{3} + 37109375 n^{2} + 19531250 n + 9765625