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

The solution to expand (e^t+e^{4t})^2 is e^{2t}+2e^{5t}+e^{8t}

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

expand

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

e^{2 t} + 2 e^{5 t} + e^{8 t}

Solution steps

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

Apply Perfect Square Formula:

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

a = e^{t}, b = e^{4 t}

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

Simplify

(e^{t})^{2} + 2 e^{t} e^{4 t} + (e^{4 t})^{2} : e^{2 t} + 2 e^{5 t} + e^{8 t}

= e^{2 t} + 2 e^{5 t} + e^{8 t}

\frac{( 1 - e ^{- 4 s} )}{s ( s ^{2} + 2 s + 17 )}

(x + y) \cdot (x^{^{'}} + z) \cdot (y + z)

\frac{7 s ^{3} - 2 ( e ^{- 2 s} + s ^{2} - s )}{s ( s ^{3} - s ^{2} - 2 )}

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

What is expand (e^t+e^{4t})^2 ?
The solution to expand (e^t+e^{4t})^2 is e^{2t}+2e^{5t}+e^{8t}