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

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

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

expand

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

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

Solution steps

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

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

Apply the distributive law:

a (b + c) = ab + a c

a = e^{x^{2}}, b = 1, c = 2 x^{3}

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

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

Multiply:

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

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

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