What is expand ln(z)(z-1)^4 ?

The solution to expand ln(z)(z-1)^4 is z^4ln(z)-4z^3ln(z)+6z^2ln(z)-4zln(z)+ln(z)

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expand ln(z)(z-1)^4

expand

ln (z) (z - 1)^{4}

z^{4} ln (z) - 4 z^{3} ln (z) + 6 z^{2} ln (z) - 4 z ln (z) + ln (z)

Solution steps

ln (z) (z - 1)^{4}

(z - 1)^{4} = z^{4} - 4 z^{3} + 6 z^{2} - 4 z + 1

= ln (z) (z^{4} - 4 z^{3} + 6 z^{2} - 4 z + 1)

Distribute parentheses

= ln (z) z^{4} + ln (z) (- 4 z^{3}) + ln (z) \cdot 6 z^{2} + ln (z) (- 4 z) + ln (z) \cdot 1

Apply minus-plus rules

+ (- a) = - a

= z^{4} ln (z) - 4 z^{3} ln (z) + 6 z^{2} ln (z) - 4 z ln (z) + 1 \cdot ln (z)

Multiply:

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

= z^{4} ln (z) - 4 z^{3} ln (z) + 6 z^{2} ln (z) - 4 z ln (z) + ln (z)

\frac{cos ( x )}{( 1 - sin ( x ) ) ^{2}}

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

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

x (y + Δ y)

e^{2 t} (t^{2} - 3 t + 2)

What is expand ln(z)(z-1)^4 ?
The solution to expand ln(z)(z-1)^4 is z^4ln(z)-4z^3ln(z)+6z^2ln(z)-4zln(z)+ln(z)