What is expand (1+2e^{-2t})^2 ?

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

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expand (1+2e^{-2t})^2

expand

(1 + 2 e^{- 2 t})^{2}

1 + 4 e^{- 2 t} + 4 e^{- 4 t}

Solution steps

(1 + 2 e^{- 2 t})^{2}

Apply Perfect Square Formula:

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

a = 1, b = 2 e^{- 2 t}

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

Simplify

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

= 1 + 4 e^{- 2 t} + 4 e^{- 4 t}

\frac{1}{3 ( x + 5 )}

\frac{2 ( n + 1 )}{n}

\frac{3}{( x ^{2} + 9 ) ( x ^{2} + 4 )}

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

P (- 2, 7, 3) Q (1, 2, - 2)

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