What is expand e^x(e^{2x}+1)^3 ?

The solution to expand e^x(e^{2x}+1)^3 is e^{7x}+3e^{5x}+3e^{3x}+e^x

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expand e^x(e^{2x}+1)^3

expand

e^{x} (e^{2 x} + 1)^{3}

e^{7 x} + 3 e^{5 x} + 3 e^{3 x} + e^{x}

Solution steps

e^{x} (e^{2 x} + 1)^{3}

(e^{2 x} + 1)^{3} = e^{6 x} + 3 e^{4 x} + 3 e^{2 x} + 1

= e^{x} (e^{6 x} + 3 e^{4 x} + 3 e^{2 x} + 1)

Distribute parentheses

= e^{x} e^{6 x} + e^{x} \cdot 3 e^{4 x} + e^{x} \cdot 3 e^{2 x} + e^{x} \cdot 1

= e^{x} e^{6 x} + 3 e^{x} e^{4 x} + 3 e^{x} e^{2 x} + 1 \cdot e^{x}

Simplify

e^{x} e^{6 x} + 3 e^{x} e^{4 x} + 3 e^{x} e^{2 x} + 1 \cdot e^{x} : e^{7 x} + 3 e^{5 x} + 3 e^{3 x} + e^{x}

= e^{7 x} + 3 e^{5 x} + 3 e^{3 x} + e^{x}

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What is expand e^x(e^{2x}+1)^3 ?
The solution to expand e^x(e^{2x}+1)^3 is e^{7x}+3e^{5x}+3e^{3x}+e^x