What is expand (3x^2+7x^3)e^{7x} ?

The solution to expand (3x^2+7x^3)e^{7x} is 3e^{7x}x^2+7e^{7x}x^3

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expand (3x^2+7x^3)e^{7x}

expand

(3 x^{2} + 7 x^{3}) e^{7 x}

3 e^{7 x} x^{2} + 7 e^{7 x} x^{3}

Solution steps

(3 x^{2} + 7 x^{3}) e^{7 x}

= e^{7 x} (3 x^{2} + 7 x^{3})

Apply the distributive law:

a (b + c) = ab + a c

a = e^{7 x}, b = 3 x^{2}, c = 7 x^{3}

= e^{7 x} \cdot 3 x^{2} + e^{7 x} \cdot 7 x^{3}

= 3 e^{7 x} x^{2} + 7 e^{7 x} x^{3}

2 (- x cos (x) + sin (x))

2 x d y + (x^{2} y^{4} + 1) y d x

(2 - \frac{x}{2})^{2}

(311.13 sin (377 t)) \cdot (3 sin (377 t) - 1.5)

\frac{d ^{3}}{d x ^{3}} ((y) (4 x^{2} - 6 x + 2))

What is expand (3x^2+7x^3)e^{7x} ?
The solution to expand (3x^2+7x^3)e^{7x} is 3e^{7x}x^2+7e^{7x}x^3