What is expand (-3x^2+4x)e^{5x} ?

The solution to expand (-3x^2+4x)e^{5x} is -3e^{5x}x^2+4e^{5x}x

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expand (-3x^2+4x)e^{5x}

expand

(- 3 x^{2} + 4 x) e^{5 x}

- 3 e^{5 x} x^{2} + 4 e^{5 x} x

Solution steps

(- 3 x^{2} + 4 x) e^{5 x}

= e^{5 x} (- 3 x^{2} + 4 x)

Apply the distributive law:

a (b + c) = ab + a c

a = e^{5 x}, b = - 3 x^{2}, c = 4 x

= e^{5 x} (- 3 x^{2}) + e^{5 x} \cdot 4 x

Apply minus-plus rules

+ (- a) = - a

= - 3 e^{5 x} x^{2} + 4 e^{5 x} x

2 (n ln (n) - n)

\frac{1}{( s ^{2} ( s ^{2} + w ^{2} ) )}

(e^{x} + 1) (12 x - 4)

\frac{s - 1}{s ( s + 1 )}

(x + b \cdot c + d \cdot e)^{2}

What is expand (-3x^2+4x)e^{5x} ?
The solution to expand (-3x^2+4x)e^{5x} is -3e^{5x}x^2+4e^{5x}x