What is expand (1+3e^{-t})^2 ?

The solution to expand (1+3e^{-t})^2 is 1+6e^{-t}+9e^{-2t}

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expand (1+3e^{-t})^2

expand

(1 + 3 e^{- t})^{2}

1 + 6 e^{- t} + 9 e^{- 2 t}

Solution steps

(1 + 3 e^{- t})^{2}

Apply Perfect Square Formula:

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

a = 1, b = 3 e^{- t}

= 1^{2} + 2 \cdot 1 \cdot 3 e^{- t} + (3 e^{- t})^{2}

Simplify

1^{2} + 2 \cdot 1 \cdot 3 e^{- t} + (3 e^{- t})^{2} : 1 + 6 e^{- t} + 9 e^{- 2 t}

= 1 + 6 e^{- t} + 9 e^{- 2 t}

2 (x + 2 y) d x + (y - x) d y

3 (x + h) - 2

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

\frac{8}{( s + 2 ) ^{2}}

\frac{( x + 5 ) ^{2}}{x ^{2} ( x - 5 )}

What is expand (1+3e^{-t})^2 ?
The solution to expand (1+3e^{-t})^2 is 1+6e^{-t}+9e^{-2t}