What is expand (4e^{-2t}-4)^2 ?

The solution to expand (4e^{-2t}-4)^2 is 16e^{-4t}-32e^{-2t}+16

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expand (4e^{-2t}-4)^2

expand

(4 e^{- 2 t} - 4)^{2}

16 e^{- 4 t} - 32 e^{- 2 t} + 16

Solution steps

(4 e^{- 2 t} - 4)^{2}

Apply Perfect Square Formula:

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

a = 4 e^{- 2 t}, b = 4

= (4 e^{- 2 t})^{2} - 2 \cdot 4 e^{- 2 t} \cdot 4 + 4^{2}

Simplify

(4 e^{- 2 t})^{2} - 2 \cdot 4 e^{- 2 t} \cdot 4 + 4^{2} : 16 e^{- 4 t} - 32 e^{- 2 t} + 16

= 16 e^{- 4 t} - 32 e^{- 2 t} + 16

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What is expand (4e^{-2t}-4)^2 ?
The solution to expand (4e^{-2t}-4)^2 is 16e^{-4t}-32e^{-2t}+16