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

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

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

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

(- 2, - 11) Y (4, 7)

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

(2 x^{2} + 3 x - 4) - (x^{2} + x = 8)

(1 - 2 x) e^{2 x}

(2 + \frac{8}{5} x)^{8}

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