展開する (x^3+x^2+1)^5

解

展開する

(x^{3} + x^{2} + 1)^{5}

x^{15} + 5 x^{14} + 10 x^{13} + 15 x^{12} + 25 x^{11} + 31 x^{10} + 30 x^{9} + 35 x^{8} + 30 x^{7} + 20 x^{6} + 20 x^{5} + 10 x^{4} + 5 x^{3} + 5 x^{2} + 1

解答ステップ

(x^{3} + x^{2} + 1)^{5}

(x^{3} + x^{2} + 1)^{5} = (x^{3} + x^{2} + 1) (x^{3} + x^{2} + 1) (x^{3} + x^{2} + 1) (x^{3} + x^{2} + 1) (x^{3} + x^{2} + 1)

= (x^{3} + x^{2} + 1) (x^{3} + x^{2} + 1) (x^{3} + x^{2} + 1) (x^{3} + x^{2} + 1) (x^{3} + x^{2} + 1)

拡張

(x^{3} + x^{2} + 1) (x^{3} + x^{2} + 1) (x^{3} + x^{2} + 1) (x^{3} + x^{2} + 1) (x^{3} + x^{2} + 1) : x^{15} + 5 x^{14} + 10 x^{13} + 15 x^{12} + 25 x^{11} + 31 x^{10} + 30 x^{9} + 35 x^{8} + 30 x^{7} + 20 x^{6} + 20 x^{5} + 10 x^{4} + 5 x^{3} + 5 x^{2} + 1

= x^{15} + 5 x^{14} + 10 x^{13} + 15 x^{12} + 25 x^{11} + 31 x^{10} + 30 x^{9} + 35 x^{8} + 30 x^{7} + 20 x^{6} + 20 x^{5} + 10 x^{4} + 5 x^{3} + 5 x^{2} + 1