What is expand (5+x)x^4e^{7x} ?

The solution to expand (5+x)x^4e^{7x} is 5e^{7x}x^4+e^{7x}x^5

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expand (5+x)x^4e^{7x}

expand

(5 + x) x^{4} e^{7 x}

5 e^{7 x} x^{4} + e^{7 x} x^{5}

Solution steps

(5 + x) x^{4} e^{7 x}

= e^{7 x} x^{4} (5 + x)

Apply the distributive law:

a (b + c) = ab + a c

a = x^{4} e^{7 x}, b = 5, c = x

= x^{4} e^{7 x} \cdot 5 + x^{4} e^{7 x} x

= 5 e^{7 x} x^{4} + e^{7 x} x^{4} x

e^{7 x} x^{4} x = e^{7 x} x^{5}

= 5 e^{7 x} x^{4} + e^{7 x} x^{5}

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What is expand (5+x)x^4e^{7x} ?
The solution to expand (5+x)x^4e^{7x} is 5e^{7x}x^4+e^{7x}x^5