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

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

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

expand

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

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

Solution steps

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

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

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

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

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

\frac{d}{d t} ((x) (cos (2 t) + sin (2 t) + \frac{1}{5} e^{t}))

(e^{2 t o + 2 a} + e^{- 2 t o - 2 a}) (e^{2 t} + e^{- 2 t})

e^{a t} u (t - 1)

\frac{d}{d z ( w )} ((w (z (w), x (w), y (w))) (x (w) + y (w)))

\frac{( 12 x - 7 ) ( 12 x + 7 )}{16}

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