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

The solution to expand (t+e^{2t})^3 is t^3+3e^{2t}t^2+3e^{4t}t+e^{6t}

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

expand

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

t^{3} + 3 e^{2 t} t^{2} + 3 e^{4 t} t + e^{6 t}

Solution steps

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

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

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

= t^{3} + 3 t^{2} e^{2 t} + 3 t (e^{2 t})^{2} + (e^{2 t})^{3}

Simplify

t^{3} + 3 t^{2} e^{2 t} + 3 t (e^{2 t})^{2} + (e^{2 t})^{3} : t^{3} + 3 e^{2 t} t^{2} + 3 e^{4 t} t + e^{6 t}

= t^{3} + 3 e^{2 t} t^{2} + 3 e^{4 t} t + e^{6 t}

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

ln (\frac{y}{1 - y})

(e^{x} + 3)^{2}

\frac{( 1 - e ^{(- 2 \cdot s)} )}{( s \cdot ( s ^{2} + 2 \cdot s + 26 ) )}

What is expand (t+e^{2t})^3 ?
The solution to expand (t+e^{2t})^3 is t^3+3e^{2t}t^2+3e^{4t}t+e^{6t}