展開する (1+x+x^2)^{10}

解

展開する

(1 + x + x^{2})^{10}

x^{20} + 10 x^{19} + 55 x^{18} + 210 x^{17} + 615 x^{16} + 1452 x^{15} + 2850 x^{14} + 4740 x^{13} + 6765 x^{12} + 8350 x^{11} + 8953 x^{10} + 8350 x^{9} + 6765 x^{8} + 4740 x^{7} + 2850 x^{6} + 1452 x^{5} + 615 x^{4} + 210 x^{3} + 55 x^{2} + 10 x + 1

解答ステップ

(1 + x + x^{2})^{10}

(1 + x + x^{2})^{10} = (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2})

= (x^{2} + x + 1) (x^{2} + x + 1) (x^{2} + x + 1) (x^{2} + x + 1) (x^{2} + x + 1) (x^{2} + x + 1) (x^{2} + x + 1) (x^{2} + x + 1) (x^{2} + x + 1) (x^{2} + x + 1)

拡張

(1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) : x^{20} + 10 x^{19} + 55 x^{18} + 210 x^{17} + 615 x^{16} + 1452 x^{15} + 2850 x^{14} + 4740 x^{13} + 6765 x^{12} + 8350 x^{11} + 8953 x^{10} + 8350 x^{9} + 6765 x^{8} + 4740 x^{7} + 2850 x^{6} + 1452 x^{5} + 615 x^{4} + 210 x^{3} + 55 x^{2} + 10 x + 1

= x^{20} + 10 x^{19} + 55 x^{18} + 210 x^{17} + 615 x^{16} + 1452 x^{15} + 2850 x^{14} + 4740 x^{13} + 6765 x^{12} + 8350 x^{11} + 8953 x^{10} + 8350 x^{9} + 6765 x^{8} + 4740 x^{7} + 2850 x^{6} + 1452 x^{5} + 615 x^{4} + 210 x^{3} + 55 x^{2} + 10 x + 1