展开 (4!)/(3!(1-(1-x))^3(1-(1-x))^1)

解答

展开

\frac{4 !}{3 ! \cdot ( 1 - ( 1 - x ) ) ^{3} \cdot ( 1 - ( 1 - x ) ) ^{1}}

\frac{4}{x ^{4}}

求解步骤

\frac{4 !}{3 ! ( 1 - ( 1 - x ) ) ^{3} ( 1 - ( 1 - x ) ) ^{1}}

使用法则

a^{1} = a

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

= \frac{4 !}{3 ! ( - ( - x + 1 ) + 1 ) ^{3} ( - ( - x + 1 ) + 1 )}

3! (1 - (1 - x))^{3} (1 - (1 - x)) = 3! (1 - (1 - x))^{4}

= \frac{4 !}{3 ! ( - ( - x + 1 ) + 1 ) ^{4}}

消去因子:

\frac{n !}{( n - m ) !} = n \cdot (n - 1) \dots (n - m + 1), n > m

\frac{4 !}{3 !} = 4

= \frac{4}{( - ( - x + 1 ) + 1 ) ^{4}}

乘开

1 - (1 - x) : x

= \frac{4}{x ^{4}}

e x p an d (\frac{1}{6} d - \frac{1}{3} q)^{2}

e x p an d (2 t + 1) (2 t)

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

e x p an d \frac{10 ( 694 - 1 )}{231}

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