What is expand sqrt(x)e^{x^2}(x^2+1)^{10} ?

The solution to expand sqrt(x)e^{x^2}(x^2+1)^{10} is

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expand sqrt(x)e^{x^2}(x^2+1)^{10}

expand

x e^{x^{2}} (x^{2} + 1)^{10}

e^{x^{2}} x^{20} x + 10 e^{x^{2}} x^{18} x + 45 e^{x^{2}} x^{16} x + 120 e^{x^{2}} x^{14} x + 210 e^{x^{2}} x^{12} x + 252 e^{x^{2}} x^{10} x + 210 e^{x^{2}} x^{8} x + 120 e^{x^{2}} x^{6} x + 45 e^{x^{2}} x^{4} x + 10 e^{x^{2}} x^{2} x + e^{x^{2}} x

Solution steps

x e^{x^{2}} (x^{2} + 1)^{10}

(x^{2} + 1)^{10} = x^{20} + 10 x^{18} + 45 x^{16} + 120 x^{14} + 210 x^{12} + 252 x^{10} + 210 x^{8} + 120 x^{6} + 45 x^{4} + 10 x^{2} + 1

= e^{x^{2}} x (x^{20} + 10 x^{18} + 45 x^{16} + 120 x^{14} + 210 x^{12} + 252 x^{10} + 210 x^{8} + 120 x^{6} + 45 x^{4} + 10 x^{2} + 1)

= e^{x^{2}} x (x^{20} + 10 x^{18} + 45 x^{16} + 120 x^{14} + 210 x^{12} + 252 x^{10} + 210 x^{8} + 120 x^{6} + 45 x^{4} + 10 x^{2} + 1)

Distribute parentheses

= x e^{x^{2}} x^{20} + x e^{x^{2}} \cdot 10 x^{18} + x e^{x^{2}} \cdot 45 x^{16} + x e^{x^{2}} \cdot 120 x^{14} + x e^{x^{2}} \cdot 210 x^{12} + x e^{x^{2}} \cdot 252 x^{10} + x e^{x^{2}} \cdot 210 x^{8} + x e^{x^{2}} \cdot 120 x^{6} + x e^{x^{2}} \cdot 45 x^{4} + x e^{x^{2}} \cdot 10 x^{2} + x e^{x^{2}} \cdot 1

= e^{x^{2}} x^{20} x + 10 e^{x^{2}} x^{18} x + 45 e^{x^{2}} x^{16} x + 120 e^{x^{2}} x^{14} x + 210 e^{x^{2}} x^{12} x + 252 e^{x^{2}} x^{10} x + 210 e^{x^{2}} x^{8} x + 120 e^{x^{2}} x^{6} x + 45 e^{x^{2}} x^{4} x + 10 e^{x^{2}} x^{2} x + 1 \cdot e^{x^{2}} x

Multiply:

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

= e^{x^{2}} x^{20} x + 10 e^{x^{2}} x^{18} x + 45 e^{x^{2}} x^{16} x + 120 e^{x^{2}} x^{14} x + 210 e^{x^{2}} x^{12} x + 252 e^{x^{2}} x^{10} x + 210 e^{x^{2}} x^{8} x + 120 e^{x^{2}} x^{6} x + 45 e^{x^{2}} x^{4} x + 10 e^{x^{2}} x^{2} x + e^{x^{2}} x

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What is expand sqrt(x)e^{x^2}(x^2+1)^{10} ?
The solution to expand sqrt(x)e^{x^2}(x^2+1)^{10} is