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

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

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

expand

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

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

Solution steps

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

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

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

Multiply:

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

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

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