展开 (1+2x-3x^2)^5

解答

展开

(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

求解步骤

(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)

乘开

(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

e x p an d \frac{2 ( 6 - 2 x ) ^{3}}{3}

e x p an d 2 (x + 9) - 18 ln (x + 9)

e x p an d (x - a)^{2} e^{a - 3 x}

e x p an d \frac{x ^{4}}{( ( x - 1 ) ( x - 3 ) ^{3} )}

e x p an d (2.5, 4, - 2) y (3, 8, - 3)