What is expand (e^{2x}-e^{4x})^2 ?

The solution to expand (e^{2x}-e^{4x})^2 is e^{4x}-2e^{6x}+e^{8x}

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expand (e^{2x}-e^{4x})^2

expand

(e^{2 x} - e^{4 x})^{2}

e^{4 x} - 2 e^{6 x} + e^{8 x}

Solution steps

(e^{2 x} - e^{4 x})^{2}

Apply Perfect Square Formula:

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

a = e^{2 x}, b = e^{4 x}

= (e^{2 x})^{2} - 2 e^{2 x} e^{4 x} + (e^{4 x})^{2}

Simplify

(e^{2 x})^{2} - 2 e^{2 x} e^{4 x} + (e^{4 x})^{2} : e^{4 x} - 2 e^{6 x} + e^{8 x}

= e^{4 x} - 2 e^{6 x} + e^{8 x}

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What is expand (e^{2x}-e^{4x})^2 ?
The solution to expand (e^{2x}-e^{4x})^2 is e^{4x}-2e^{6x}+e^{8x}