What is expand (3e^{-2t}-4e^{-4t})^2 ?

The solution to expand (3e^{-2t}-4e^{-4t})^2 is 9e^{-4t}-24e^{-6t}+16e^{-8t}

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expand (3e^{-2t}-4e^{-4t})^2

expand

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

9 e^{- 4 t} - 24 e^{- 6 t} + 16 e^{- 8 t}

Solution steps

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

Apply Perfect Square Formula:

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

a = 3 e^{- 2 t}, b = 4 e^{- 4 t}

= (3 e^{- 2 t})^{2} - 2 \cdot 3 e^{- 2 t} \cdot 4 e^{- 4 t} + (4 e^{- 4 t})^{2}

Simplify

(3 e^{- 2 t})^{2} - 2 \cdot 3 e^{- 2 t} \cdot 4 e^{- 4 t} + (4 e^{- 4 t})^{2} : 9 e^{- 4 t} - 24 e^{- 6 t} + 16 e^{- 8 t}

= 9 e^{- 4 t} - 24 e^{- 6 t} + 16 e^{- 8 t}

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What is expand (3e^{-2t}-4e^{-4t})^2 ?
The solution to expand (3e^{-2t}-4e^{-4t})^2 is 9e^{-4t}-24e^{-6t}+16e^{-8t}