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

The solution to expand e^x(e^2x+1)^3 is e^{6+x}x^3+3e^{4+x}x^2+3e^{2+x}x+e^x

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

expand

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

e^{6 + x} x^{3} + 3 e^{4 + x} x^{2} + 3 e^{2 + x} x + e^{x}

Solution steps

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

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

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

Distribute parentheses

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

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

Simplify

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

= e^{6 + x} x^{3} + 3 e^{4 + x} x^{2} + 3 e^{2 + x} x + e^{x}

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

\frac{5 x ^{2} - 16 x + 2}{3 x ( x - 1 )}

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

y^{'} (x) - (y^{2} + 1) sin (x)

\frac{( p \cdot ( l - a ) )}{l}

What is expand e^x(e^2x+1)^3 ?
The solution to expand e^x(e^2x+1)^3 is e^{6+x}x^3+3e^{4+x}x^2+3e^{2+x}x+e^x