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

The solution to expand (z-1)(z-e^{-T}) is z^2-e^{-T}z-z+e^{-T}

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expand (z-1)(z-e^{-T})

expand

(z - 1) (z - e^{- T})

z^{2} - e^{- T} z - z + e^{- T}

Solution steps

(z - 1) (z - e^{- T})

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

a = z, b = - 1, c = z, d = - e^{- T}

= zz + z (- e^{- T}) + (- 1) z + (- 1) (- e^{- T})

Apply minus-plus rules

+ (- a) = - a, (- a) (- b) = ab

= zz - e^{- T} z - 1 \cdot z + 1 \cdot e^{- T}

Simplify

zz - e^{- T} z - 1 \cdot z + 1 \cdot e^{- T} : z^{2} - e^{- T} z - z + e^{- T}

= z^{2} - e^{- T} z - z + e^{- T}

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