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

The solution to expand x(x^3e^{3x}+2) is e^{3x}x^4+2x

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

expand

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

e^{3 x} x^{4} + 2 x

Solution steps

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

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

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

e^{3 x} x^{3} x = e^{3 x} x^{4}

= e^{3 x} x^{4} + 2 x

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What is expand x(x^3e^{3x}+2) ?
The solution to expand x(x^3e^{3x}+2) is e^{3x}x^4+2x