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

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

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

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

\frac{4 ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{2}}

(2 - \frac{x}{16})^{9}

(2 + 3) (5 - 7)

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

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