展开 (t+x-1)^5

解答

展开

(t + x - 1)^{5}

t^{5} + 5 t^{4} x - 5 t^{4} + 10 t^{3} x^{2} - 20 t^{3} x + 10 t^{3} + 10 t^{2} x^{3} - 30 t^{2} x^{2} + 30 t^{2} x - 10 t^{2} + 5 t x^{4} - 20 t x^{3} + 30 t x^{2} - 20 t x + 5 t + x^{5} - 5 x^{4} + 10 x^{3} - 10 x^{2} + 5 x - 1

求解步骤

(t + x - 1)^{5}

(t + x - 1)^{5} = (t + x - 1) (t + x - 1) (t + x - 1) (t + x - 1) (t + x - 1)

= (t + x - 1) (t + x - 1) (t + x - 1) (t + x - 1) (t + x - 1)

乘开

(t + x - 1) (t + x - 1) (t + x - 1) (t + x - 1) (t + x - 1) : t^{5} + 5 t^{4} x - 5 t^{4} + 10 t^{3} x^{2} - 20 t^{3} x + 10 t^{3} + 10 t^{2} x^{3} - 30 t^{2} x^{2} + 30 t^{2} x - 10 t^{2} + 5 t x^{4} - 20 t x^{3} + 30 t x^{2} - 20 t x + 5 t + x^{5} - 5 x^{4} + 10 x^{3} - 10 x^{2} + 5 x - 1

= t^{5} + 5 t^{4} x - 5 t^{4} + 10 t^{3} x^{2} - 20 t^{3} x + 10 t^{3} + 10 t^{2} x^{3} - 30 t^{2} x^{2} + 30 t^{2} x - 10 t^{2} + 5 t x^{4} - 20 t x^{3} + 30 t x^{2} - 20 t x + 5 t + x^{5} - 5 x^{4} + 10 x^{3} - 10 x^{2} + 5 x - 1

e x p an d \frac{5 ( x - 1 )}{k}

e x p an d ((- y + 3) (- y^{2} + 9)) y

e x p an d \frac{x ^{4} + ( p - 3 ) \cdot x ^{2} + ( q + 3 )}{x ^{2} + x + 1}

e x p an d \frac{1 - s ^{2} + 5 s}{s ( s - 5 ) ( s + 2 )}

e x p an d (\frac{Q ( s , h ) s}{ma} - h^{1} = - h^{2}) \cdot (- 1)