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

The solution to expand (1+e^{2t})^3 is 1+3e^{2t}+3e^{4t}+e^{6t}

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

expand

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

1 + 3 e^{2 t} + 3 e^{4 t} + e^{6 t}

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

1^{3} + 3 \cdot 1^{2} e^{2 t} + 3 \cdot 1 \cdot (e^{2 t})^{2} + (e^{2 t})^{3} : 1 + 3 e^{2 t} + 3 e^{4 t} + e^{6 t}

= 1 + 3 e^{2 t} + 3 e^{4 t} + e^{6 t}

\frac{2 ( n + 1 ) ( 2 n + 1 )}{3 n}

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

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

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

\frac{( 2 x - 3 ) ^{2}}{4}

What is expand (1+e^{2t})^3 ?
The solution to expand (1+e^{2t})^3 is 1+3e^{2t}+3e^{4t}+e^{6t}