What is simplify-2e^{-2t}(4e^{2t}+4te^{2t}) ?

The solution to simplify-2e^{-2t}(4e^{2t}+4te^{2t}) is -8(t+1)

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simplify-2e^{-2t}(4e^{2t}+4te^{2t})

simplify

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

- 8 (t + 1)

Solution steps

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

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= - 2 \cdot \frac{1}{e ^{2 t}} (4 e^{2 t} t + 4 e^{2 t})

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{1 \cdot 2 ( 4 e ^{2 t} + 4 t e ^{2 t} )}{e ^{2 t}}

Multiply the numbers:

1 \cdot 2 = 2

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

Cancel

\frac{2 ( 4 e ^{2 t} + 4 t e ^{2 t} )}{e ^{2 t}} : 8 (t + 1)

= - 8 (t + 1)

7.5 x 1 0^{- 6}

2.91 \cdot 1 0^{- 5}

7.5 x 1 0^{- 4}

- 3 - 243

e^{- \frac{x}{2}} \cdot e^{x}

What is simplify-2e^{-2t}(4e^{2t}+4te^{2t}) ?
The solution to simplify-2e^{-2t}(4e^{2t}+4te^{2t}) is -8(t+1)