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

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

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

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

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