What is (x^s*(1-x)^{1-s})*x^{a-1}*(1-x)^{1-b} ?

The solution to (x^s*(1-x)^{1-s})*x^{a-1}*(1-x)^{1-b} is x^{s+a-1}(-x+1)^{-s+2-b}

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simplify (x^s(1-x)^{1-s})x^{a-1}*(1-x)^{1-b}

simplify

(x^{s} \cdot (1 - x)^{1 - s}) \cdot x^{a - 1} \cdot (1 - x)^{1 - b}

x^{s + a - 1} (- x + 1)^{- s + 2 - b}

Solution steps

(x^{s} (1 - x)^{1 - s}) x^{a - 1} (1 - x)^{1 - b}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

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

= x^{s} x^{a - 1} (1 - x)^{1 - s + 1 - b}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

x^{s} x^{a - 1} = x^{s + a - 1}

= x^{s + a - 1} (1 - x)^{1 - s + 1 - b}

Simplify

1 - s + 1 - b : - s + 2 - b

= x^{s + a - 1} (- x + 1)^{- s + 2 - b}

2^{e^{5 t} + (\frac{1}{2} e^{- t})}

e^{- 2} \frac{2 ^{3}}{3 !}

- \frac{1}{2} e^{- \frac{x}{2}}

\frac{d}{d x} (5 x - 4 y)

What is (x^s*(1-x)^{1-s})*x^{a-1}*(1-x)^{1-b} ?
The solution to (x^s*(1-x)^{1-s})*x^{a-1}*(1-x)^{1-b} is x^{s+a-1}(-x+1)^{-s+2-b}