What is expand ln(z)(z-1)^5 ?

The solution to expand ln(z)(z-1)^5 is z^5ln(z)-5z^4ln(z)+10z^3ln(z)-10z^2ln(z)+5zln(z)-ln(z)

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expand ln(z)(z-1)^5

expand

ln (z) (z - 1)^{5}

z^{5} ln (z) - 5 z^{4} ln (z) + 10 z^{3} ln (z) - 10 z^{2} ln (z) + 5 z ln (z) - ln (z)

Solution steps

ln (z) (z - 1)^{5}

(z - 1)^{5} = z^{5} - 5 z^{4} + 10 z^{3} - 10 z^{2} + 5 z - 1

= ln (z) (z^{5} - 5 z^{4} + 10 z^{3} - 10 z^{2} + 5 z - 1)

Distribute parentheses

= ln (z) z^{5} + ln (z) (- 5 z^{4}) + ln (z) \cdot 10 z^{3} + ln (z) (- 10 z^{2}) + ln (z) \cdot 5 z + ln (z) (- 1)

Apply minus-plus rules

+ (- a) = - a

= z^{5} ln (z) - 5 z^{4} ln (z) + 10 z^{3} ln (z) - 10 z^{2} ln (z) + 5 z ln (z) - 1 \cdot ln (z)

Multiply:

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

= z^{5} ln (z) - 5 z^{4} ln (z) + 10 z^{3} ln (z) - 10 z^{2} ln (z) + 5 z ln (z) - ln (z)

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What is expand ln(z)(z-1)^5 ?
The solution to expand ln(z)(z-1)^5 is z^5ln(z)-5z^4ln(z)+10z^3ln(z)-10z^2ln(z)+5zln(z)-ln(z)