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

The solution to expand (e^{4x}-2e^x)^2 is e^{8x}-4e^{5x}+4e^{2x}

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

expand

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

e^{8 x} - 4 e^{5 x} + 4 e^{2 x}

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

(e^{4 x})^{2} - 2 e^{4 x} \cdot 2 e^{x} + (2 e^{x})^{2} : e^{8 x} - 4 e^{5 x} + 4 e^{2 x}

= e^{8 x} - 4 e^{5 x} + 4 e^{2 x}

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What is expand (e^{4x}-2e^x)^2 ?
The solution to expand (e^{4x}-2e^x)^2 is e^{8x}-4e^{5x}+4e^{2x}