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

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

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

expand

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

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

Solution steps

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

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

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

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

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

11 (6 + 3)

- (21 + 4) \cdot (12 x^{5} - 5)

2 (x + 5 - 5 ln ∣ x + 5 ∣)

\frac{d}{d x} (2 x e^{x}) + (e^{x}) (x^{2} - 5)

m (1 - cos (x))

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