What is expand ln(z)(z-1)^3 ?

The solution to expand ln(z)(z-1)^3 is z^3ln(z)-3z^2ln(z)+3zln(z)-ln(z)

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expand ln(z)(z-1)^3

expand

ln (z) (z - 1)^{3}

z^{3} ln (z) - 3 z^{2} ln (z) + 3 z ln (z) - ln (z)

Solution steps

ln (z) (z - 1)^{3}

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

= ln (z) (z^{3} - 3 z^{2} + 3 z - 1)

Distribute parentheses

= ln (z) z^{3} + ln (z) (- 3 z^{2}) + ln (z) \cdot 3 z + ln (z) (- 1)

Apply minus-plus rules

+ (- a) = - a

= z^{3} ln (z) - 3 z^{2} ln (z) + 3 z ln (z) - 1 \cdot ln (z)

Multiply:

1 \cdot ln (z) = ln (z)

= z^{3} ln (z) - 3 z^{2} ln (z) + 3 z ln (z) - ln (z)

\frac{d}{d t} ((x) (- x - y (x, t) - t))

\frac{2 x - 1}{( a x + b ) ( c x + d ) ^{2}}

\frac{( ( x + h ) ^{\frac{2}{3}} - x ^{\frac{2}{3}} )}{h}

\frac{2 ( x + 9 ) ( x - 1 )}{( x + 4 ) ( x - 2 )}

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

What is expand ln(z)(z-1)^3 ?
The solution to expand ln(z)(z-1)^3 is z^3ln(z)-3z^2ln(z)+3zln(z)-ln(z)