展開する (x^3-5x^2+1)^6

解

展開する

(x^{3} - 5 x^{2} + 1)^{6}

x^{18} - 30 x^{17} + 375 x^{16} - 2494 x^{15} + 9225 x^{14} - 17250 x^{13} + 8140 x^{12} + 18450 x^{11} - 16500 x^{10} - 7480 x^{9} + 9075 x^{8} + 1500 x^{7} - 2485 x^{6} - 150 x^{5} + 375 x^{4} + 6 x^{3} - 30 x^{2} + 1

解答ステップ

(x^{3} - 5 x^{2} + 1)^{6}

(x^{3} - 5 x^{2} + 1)^{6} = (x^{3} - 5 x^{2} + 1) (x^{3} - 5 x^{2} + 1) (x^{3} - 5 x^{2} + 1) (x^{3} - 5 x^{2} + 1) (x^{3} - 5 x^{2} + 1) (x^{3} - 5 x^{2} + 1)

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

拡張

(x^{3} - 5 x^{2} + 1) (x^{3} - 5 x^{2} + 1) (x^{3} - 5 x^{2} + 1) (x^{3} - 5 x^{2} + 1) (x^{3} - 5 x^{2} + 1) (x^{3} - 5 x^{2} + 1) : x^{18} - 30 x^{17} + 375 x^{16} - 2494 x^{15} + 9225 x^{14} - 17250 x^{13} + 8140 x^{12} + 18450 x^{11} - 16500 x^{10} - 7480 x^{9} + 9075 x^{8} + 1500 x^{7} - 2485 x^{6} - 150 x^{5} + 375 x^{4} + 6 x^{3} - 30 x^{2} + 1

= x^{18} - 30 x^{17} + 375 x^{16} - 2494 x^{15} + 9225 x^{14} - 17250 x^{13} + 8140 x^{12} + 18450 x^{11} - 16500 x^{10} - 7480 x^{9} + 9075 x^{8} + 1500 x^{7} - 2485 x^{6} - 150 x^{5} + 375 x^{4} + 6 x^{3} - 30 x^{2} + 1