What is expand ln(z)(z-1)^2 ?

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

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expand ln(z)(z-1)^2

expand

ln (z) (z - 1)^{2}

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

Solution steps

ln (z) (z - 1)^{2}

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

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

Distribute parentheses

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

Apply minus-plus rules

+ (- a) = - a

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

Multiply:

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

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

(1 + cos (θ)) (csc (θ) - cot (θ))

\frac{s}{( s ^{2} + a ^{2} ) ( s ^{2} + b ^{2} )}

\frac{1}{( 1 + x ) ^{3}}

cos (θ) (csc (θ) - sec (θ)) + 1

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