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

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

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

expand

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

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

Solution steps

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

Apply the distributive law:

a (b + c) = ab + a c

a = e^{x^{2} + 1}, b = 1, c = 2 x^{2}

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

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

Multiply:

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

= e^{x^{2} + 1} + 2 e^{x^{2} + 1} x^{2}

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x^{2} y^{''} (x) + x y^{'} (x) + (x^{2} - \frac{1}{4}) y - x^{\frac{3}{2}}

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