What is expand (e^{2x}-e^x)^2 ?

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

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

expand

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

e^{4 x} - 2 e^{3 x} + e^{2 x}

Solution steps

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

Apply Perfect Square Formula:

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

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

= (e^{2 x})^{2} - 2 e^{2 x} e^{x} + (e^{x})^{2}

Simplify

(e^{2 x})^{2} - 2 e^{2 x} e^{x} + (e^{x})^{2} : e^{4 x} - 2 e^{3 x} + e^{2 x}

= e^{4 x} - 2 e^{3 x} + e^{2 x}

\frac{4 s ^{2} + 36 + s ^{3} + 16 s}{( s ^{2} + 9 ) ( s ^{2} + 16 )}

\frac{1}{3 \cdot x ( x - 8 )}

\frac{1}{5} (15 + 10 x - 5)

(y + \frac{b}{a}) \cdot (e^{a t} - \frac{b}{a})

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