展開する (1+x^4+x^6)^7

解

展開する

(1 + x^{4} + x^{6})^{7}

x^{42} + 7 x^{40} + 21 x^{38} + 42 x^{36} + 77 x^{34} + 126 x^{32} + 168 x^{30} + 211 x^{28} + 252 x^{26} + 252 x^{24} + 245 x^{22} + 231 x^{20} + 175 x^{18} + 140 x^{16} + 105 x^{14} + 56 x^{12} + 42 x^{10} + 21 x^{8} + 7 x^{6} + 7 x^{4} + 1

解答ステップ

(1 + x^{4} + x^{6})^{7}

(1 + x^{4} + x^{6})^{7} = (1 + x^{4} + x^{6}) (1 + x^{4} + x^{6}) (1 + x^{4} + x^{6}) (1 + x^{4} + x^{6}) (1 + x^{4} + x^{6}) (1 + x^{4} + x^{6}) (1 + x^{4} + x^{6})

= (x^{6} + x^{4} + 1) (x^{6} + x^{4} + 1) (x^{6} + x^{4} + 1) (x^{6} + x^{4} + 1) (x^{6} + x^{4} + 1) (x^{6} + x^{4} + 1) (x^{6} + x^{4} + 1)

拡張

(1 + x^{4} + x^{6}) (1 + x^{4} + x^{6}) (1 + x^{4} + x^{6}) (1 + x^{4} + x^{6}) (1 + x^{4} + x^{6}) (1 + x^{4} + x^{6}) (1 + x^{4} + x^{6}) : x^{42} + 7 x^{40} + 21 x^{38} + 42 x^{36} + 77 x^{34} + 126 x^{32} + 168 x^{30} + 211 x^{28} + 252 x^{26} + 252 x^{24} + 245 x^{22} + 231 x^{20} + 175 x^{18} + 140 x^{16} + 105 x^{14} + 56 x^{12} + 42 x^{10} + 21 x^{8} + 7 x^{6} + 7 x^{4} + 1

= x^{42} + 7 x^{40} + 21 x^{38} + 42 x^{36} + 77 x^{34} + 126 x^{32} + 168 x^{30} + 211 x^{28} + 252 x^{26} + 252 x^{24} + 245 x^{22} + 231 x^{20} + 175 x^{18} + 140 x^{16} + 105 x^{14} + 56 x^{12} + 42 x^{10} + 21 x^{8} + 7 x^{6} + 7 x^{4} + 1