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

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

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

expand

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

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

Solution steps

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

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

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

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

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

\frac{2 ( t ^{2} + 1 - 2 t )}{( t ^{2} + 1 ) ^{2}}

\frac{5 ( 5 + 65 )}{4}

\frac{( a + b ) ( a - b )}{2 a ( 1 - b )}

x (x + \frac{1}{2}) (x - \frac{1}{2})

(- i, - 2 j, 3 k) \cdot (- 3 i, 0 j, k)

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