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}

(1, - 2) y (2, - 2)

\frac{x ^{3}}{( x ^{2} + 1 ) ^{2}}

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

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

\frac{\partial}{\partial u} ((x) (a u + b v))

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