What is expand ds(s-1)^3 ?

The solution to expand ds(s-1)^3 is s^3ds-3s^2ds+3sds-ds

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expand ds(s-1)^3

expand

d s (s - 1)^{3}

s^{3} d s - 3 s^{2} d s + 3 s d s - d s

Solution steps

d s (s - 1)^{3}

(s - 1)^{3} = s^{3} - 3 s^{2} + 3 s - 1

= d s (s^{3} - 3 s^{2} + 3 s - 1)

Distribute parentheses

= d s s^{3} + d s (- 3 s^{2}) + d s \cdot 3 s + d s (- 1)

Apply minus-plus rules

+ (- a) = - a

= s^{3} d s - 3 s^{2} d s + 3 s d s - 1 \cdot d s

Multiply:

1 \cdot d s = d s

= s^{3} d s - 3 s^{2} d s + 3 s d s - d s

\frac{( ln ( x ) + 1 ) ( 1 - ln ( x ) ) + ln ( x )}{( 1 - ln ( x ) ) ^{2}}

\frac{( - 3 y + 3 d + 2 ) ^{2}}{16}

\frac{e ^{- s - 2}}{( s - 2 ) ( 2 s + 2 )}

e^{x} \cdot (- e^{- x - 1} - \frac{e ^{- 2 x} x}{2} + \frac{1}{4} e^{- 2 x})

e x p an (1 + 4 x)^{7}

What is expand ds(s-1)^3 ?
The solution to expand ds(s-1)^3 is s^3ds-3s^2ds+3sds-ds