展開する (1+2x+3x^2)^6

解

展開する

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

729 x^{12} + 2916 x^{11} + 6318 x^{10} + 9180 x^{9} + 9855 x^{8} + 8136 x^{7} + 5284 x^{6} + 2712 x^{5} + 1095 x^{4} + 340 x^{3} + 78 x^{2} + 12 x + 1

解答ステップ

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

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

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

拡張

(1 + 2 x + 3 x^{2}) (1 + 2 x + 3 x^{2}) (1 + 2 x + 3 x^{2}) (1 + 2 x + 3 x^{2}) (1 + 2 x + 3 x^{2}) (1 + 2 x + 3 x^{2}) : 729 x^{12} + 2916 x^{11} + 6318 x^{10} + 9180 x^{9} + 9855 x^{8} + 8136 x^{7} + 5284 x^{6} + 2712 x^{5} + 1095 x^{4} + 340 x^{3} + 78 x^{2} + 12 x + 1

= 729 x^{12} + 2916 x^{11} + 6318 x^{10} + 9180 x^{9} + 9855 x^{8} + 8136 x^{7} + 5284 x^{6} + 2712 x^{5} + 1095 x^{4} + 340 x^{3} + 78 x^{2} + 12 x + 1