What is expand (4x^3e^x)(x^2+1) ?

The solution to expand (4x^3e^x)(x^2+1) is 4e^xx^5+4e^xx^3

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expand (4x^3e^x)(x^2+1)

expand

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

4 e^{x} x^{5} + 4 e^{x} x^{3}

Solution steps

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

= (4 e^{x} x^{3}) (x^{2} + 1)

Apply the distributive law:

a (b + c) = ab + a c

a = (4 x^{3} e^{x}), b = x^{2}, c = 1

= (4 x^{3} e^{x}) x^{2} + (4 x^{3} e^{x}) \cdot 1

= x^{2} (4 e^{x} x^{3}) + 1 \cdot (4 e^{x} x^{3})

Simplify

x^{2} (4 e^{x} x^{3}) + 1 \cdot (4 e^{x} x^{3}) : 4 e^{x} x^{5} + 4 e^{x} x^{3}

= 4 e^{x} x^{5} + 4 e^{x} x^{3}

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(8 - 2 x)^{\circ} (7 x + 3) (x)

What is expand (4x^3e^x)(x^2+1) ?
The solution to expand (4x^3e^x)(x^2+1) is 4e^xx^5+4e^xx^3