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

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

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

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

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

(x - 2)^{2}

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

(2 + i)^{4}

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

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