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

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

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

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

\frac{( y - 1 ) ^{2}}{2}

\frac{4 ( 3 - 4 j )}{5 ( - 2 + 3 j )}

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\frac{4 x ^{2} + 3 x + 1}{( x + 3 ) ( 3 x + 1 )}

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

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