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

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

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expand (x^2+1)^2xe^{2x}

expand

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

e^{2 x} x^{5} + 2 e^{2 x} x^{3} + e^{2 x} x

Solution steps

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

(x^{2} + 1)^{2} = x^{4} + 2 x^{2} + 1

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

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

Distribute parentheses

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

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

Simplify

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

= e^{2 x} x^{5} + 2 e^{2 x} x^{3} + e^{2 x} x

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