展开 (1+x-x^2)^7

解答

展开

(1 + x - x^{2})^{7}

- x^{14} + 7 x^{13} - 14 x^{12} - 7 x^{11} + 49 x^{10} - 14 x^{9} - 77 x^{8} + 29 x^{7} + 77 x^{6} - 14 x^{5} - 49 x^{4} - 7 x^{3} + 14 x^{2} + 7 x + 1

求解步骤

(1 + x - x^{2})^{7}

(1 + x - x^{2})^{7} = (1 + x - x^{2}) (1 + x - x^{2}) (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) (- x^{2} + x + 1) (- x^{2} + x + 1)

乘开

(1 + x - x^{2}) (1 + x - x^{2}) (1 + x - x^{2}) (1 + x - x^{2}) (1 + x - x^{2}) (1 + x - x^{2}) (1 + x - x^{2}) : - x^{14} + 7 x^{13} - 14 x^{12} - 7 x^{11} + 49 x^{10} - 14 x^{9} - 77 x^{8} + 29 x^{7} + 77 x^{6} - 14 x^{5} - 49 x^{4} - 7 x^{3} + 14 x^{2} + 7 x + 1

= - x^{14} + 7 x^{13} - 14 x^{12} - 7 x^{11} + 49 x^{10} - 14 x^{9} - 77 x^{8} + 29 x^{7} + 77 x^{6} - 14 x^{5} - 49 x^{4} - 7 x^{3} + 14 x^{2} + 7 x + 1

e x p an d (e^{x} x - e^{x}) (2 x - 1)

e x p an d A (2, - 3) B (4, 6)

e x p an d \frac{4 ( - 2 n + k )}{n}

e x p an d \frac{x ( x ^{2} + 1 )}{x ^{2} - 1}

e x p an d (x + d x) (y cos (x))