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

The solution to expand (2e^{-4t}+sin(t))^2 is 4e^{-8t}+4e^{-4t}sin(t)+sin^2(t)

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

expand

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

4 e^{- 8 t} + 4 e^{- 4 t} sin (t) + sin^{2} (t)

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

(2 e^{- 4 t})^{2} + 2 \cdot 2 e^{- 4 t} sin (t) + sin^{2} (t) : 4 e^{- 8 t} + 4 e^{- 4 t} sin (t) + sin^{2} (t)

= 4 e^{- 8 t} + 4 e^{- 4 t} sin (t) + sin^{2} (t)

\frac{3 s - 2}{s ^{3} ( s ^{2} + 4 )}

\frac{1 - x + 2 x ^{2} - x ^{3}}{x ( x ^{2} + 1 ) ^{2}}

(sin (2 x) + cos (2 x))^{2}

(3 x - \frac{1}{2 x})^{6}

What is expand (2e^{-4t}+sin(t))^2 ?
The solution to expand (2e^{-4t}+sin(t))^2 is 4e^{-8t}+4e^{-4t}sin(t)+sin^2(t)