What is expand (4!)/(3!*(1-(1-x))^3*(1-(1-x))^1) ?

The solution to expand (4!)/(3!*(1-(1-x))^3*(1-(1-x))^1) is 4/(x^4)

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expand (4!)/(3!(1-(1-x))^3(1-(1-x))^1)

expand

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

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

Solution steps

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

Apply rule

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}}

Cancel the factorials:

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

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

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

Expand

1 - (1 - x) : x

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

(\frac{1}{6} d - \frac{1}{3} q)^{2}

\frac{( 0.5 + x ) ( 0.4 + x )}{( 0.5 - x ) ( 0.45 - x )}

(2 t + 1) (2 t)

x (1 - ln (x))^{2}

\frac{10 ( 694 - 1 )}{231}

What is expand (4!)/(3!*(1-(1-x))^3*(1-(1-x))^1) ?
The solution to expand (4!)/(3!*(1-(1-x))^3*(1-(1-x))^1) is 4/(x^4)