What is expand (1-e^{-t/(RC)})^2 ?

The solution to expand (1-e^{-t/(RC)})^2 is 1-2e^{-t/(RC)}+e^{-(2t)/(RC)}

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expand (1-e^{-t/(RC)})^2

expand

(1 - e^{- \frac{t}{RC}})^{2}

1 - 2 e^{- \frac{t}{RC}} + e^{- \frac{2 t}{RC}}

Solution steps

(1 - e^{- \frac{t}{RC}})^{2}

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

a = 1, b = e^{- \frac{t}{RC}}

= 1^{2} - 2 \cdot 1 \cdot e^{- \frac{t}{RC}} + (e^{- \frac{t}{RC}})^{2}

Simplify

1^{2} - 2 \cdot 1 \cdot e^{- \frac{t}{RC}} + (e^{- \frac{t}{RC}})^{2} : 1 - 2 e^{- \frac{t}{RC}} + e^{- \frac{2 t}{RC}}

= 1 - 2 e^{- \frac{t}{RC}} + e^{- \frac{2 t}{RC}}

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- \frac{( x + 12 ) ( x + 8 ) ( x - 0 ) ( x - 12 )}{10240}

What is expand (1-e^{-t/(RC)})^2 ?
The solution to expand (1-e^{-t/(RC)})^2 is 1-2e^{-t/(RC)}+e^{-(2t)/(RC)}