展開する (1+2x-3x^2)^5

解

展開する

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

- 243 x^{10} + 810 x^{9} - 675 x^{8} - 360 x^{7} + 570 x^{6} + 92 x^{5} - 190 x^{4} - 40 x^{3} + 25 x^{2} + 10 x + 1

解答ステップ

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

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

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}) : - 243 x^{10} + 810 x^{9} - 675 x^{8} - 360 x^{7} + 570 x^{6} + 92 x^{5} - 190 x^{4} - 40 x^{3} + 25 x^{2} + 10 x + 1

= - 243 x^{10} + 810 x^{9} - 675 x^{8} - 360 x^{7} + 570 x^{6} + 92 x^{5} - 190 x^{4} - 40 x^{3} + 25 x^{2} + 10 x + 1