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

The solution to expand 1/(z^2(z-2)^2) is 1/(z^4-4z^3+4z^2)

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

expand

\frac{1}{z ^{2} ( z - 2 ) ^{2}}

\frac{1}{z ^{4} - 4 z ^{3} + 4 z ^{2}}

Solution steps

\frac{1}{z ^{2} ( z - 2 ) ^{2}}

(z - 2)^{2} = z^{2} - 4 z + 4

= \frac{1}{z ^{2} ( z ^{2} - 4 z + 4 )}

Expand

z^{2} (z^{2} - 4 z + 4) : z^{4} - 4 z^{3} + 4 z^{2}

= \frac{1}{z ^{4} - 4 z ^{3} + 4 z ^{2}}

\frac{( x ^{2} - x - 1 ) ^{3}}{2 x - 1}

(e^{2 i θ} - 2 + e^{- 2 i θ}) (e^{- i θ} - e^{i θ})

2 (x + Δ x)^{2} + 4 (x + Δ x)

(x + y + z + w + u)^{3}

2 (x - 2 y = 10)

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