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

The solution to expand (-2e^{-2t}-3e^{3t})^2 is 4e^{-4t}+12e^t+9e^{6t}

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

expand

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

4 e^{- 4 t} + 12 e^{t} + 9 e^{6 t}

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

(- 2 e^{- 2 t})^{2} - 2 (- 2 e^{- 2 t}) \cdot 3 e^{3 t} + (3 e^{3 t})^{2} : 4 e^{- 4 t} + 12 e^{t} + 9 e^{6 t}

= 4 e^{- 4 t} + 12 e^{t} + 9 e^{6 t}

\frac{d}{d t} ((x) (x^{2} + y^{2}))

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(x - 2 + 3) (x - 2 - 3)

What is expand (-2e^{-2t}-3e^{3t})^2 ?
The solution to expand (-2e^{-2t}-3e^{3t})^2 is 4e^{-4t}+12e^t+9e^{6t}