What is expand (4+x)x^3e^{4x} ?

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

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expand (4+x)x^3e^{4x}

expand

(4 + x) x^{3} e^{4 x}

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

Solution steps

(4 + x) x^{3} e^{4 x}

= e^{4 x} x^{3} (4 + x)

Apply the distributive law:

a (b + c) = ab + a c

a = x^{3} e^{4 x}, b = 4, c = x

= x^{3} e^{4 x} \cdot 4 + x^{3} e^{4 x} x

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

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

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

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