What is expand-e^{5x}*5(x^2+3x) ?

The solution to expand-e^{5x}*5(x^2+3x) is -5e^{5x}x^2-15e^{5x}x

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expand-e^{5x}*5(x^2+3x)

expand

- e^{5 x} \cdot 5 (x^{2} + 3 x)

- 5 e^{5 x} x^{2} - 15 e^{5 x} x

Solution steps

- e^{5 x} \cdot 5 (x^{2} + 3 x)

= - 5 e^{5 x} (x^{2} + 3 x)

Apply the distributive law:

a (b + c) = ab + a c

a = - e^{5 x} \cdot 5, b = x^{2}, c = 3 x

= - e^{5 x} \cdot 5 x^{2} + (- e^{5 x} \cdot 5) \cdot 3 x

Apply minus-plus rules

+ (- a) = - a

= - 5 e^{5 x} x^{2} - 5 \cdot 3 e^{5 x} x

Multiply the numbers:

5 \cdot 3 = 15

= - 5 e^{5 x} x^{2} - 15 e^{5 x} x

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What is expand-e^{5x}*5(x^2+3x) ?
The solution to expand-e^{5x}*5(x^2+3x) is -5e^{5x}x^2-15e^{5x}x