What is expand (1-z^{-1})(1-z^{-1})^2 ?

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

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

expand

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

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

Solution steps

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

Apply the distributive law:

a (b - c) = ab - a c

a = (1 - z^{- 1})^{2}, b = 1, c = z^{- 1}

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

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

Simplify

1 \cdot (1 - z^{- 1})^{2} - z^{- 1} (1 - z^{- 1})^{2} : - \frac{3}{z} + \frac{3}{z ^{2}} - \frac{1}{z ^{3}} + 1

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

\frac{( 3 x ^{2} + 7 ) ^{6}}{( 5 x ^{3} + 1 ) ^{4}}

(4 - x^{2}) d x

\frac{1}{( x ^{2} + 6 x + 5 ) ^{2}}

(2 x - 5) (x + 1)

\frac{( x + 3 ) ( x + 1 ) ( x - 1 )}{( x + 2 ) ( x - 4 )}

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