展開する (1+x+x^2)^5

解

展開する

(1 + x + x^{2})^{5}

x^{10} + 5 x^{9} + 15 x^{8} + 30 x^{7} + 45 x^{6} + 51 x^{5} + 45 x^{4} + 30 x^{3} + 15 x^{2} + 5 x + 1

解答ステップ

(1 + x + x^{2})^{5}

(1 + x + x^{2})^{5} = (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)

拡張

(1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) : x^{10} + 5 x^{9} + 15 x^{8} + 30 x^{7} + 45 x^{6} + 51 x^{5} + 45 x^{4} + 30 x^{3} + 15 x^{2} + 5 x + 1

= x^{10} + 5 x^{9} + 15 x^{8} + 30 x^{7} + 45 x^{6} + 51 x^{5} + 45 x^{4} + 30 x^{3} + 15 x^{2} + 5 x + 1