What is expand (e^x+xe^x)^2 ?

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

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expand (e^x+xe^x)^2

expand

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

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

Solution steps

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

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

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

a = e^{x}, b = x e^{x}

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

Simplify

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

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

(2 x + 6) sin (x)

(a + b) (a - b)

- \frac{cos ( θ ) ( - cos ( θ ) + 2 ) - sin ^{2} ( θ )}{2 sin ( θ )}

x^{2} - 2 x (x^{3} + 7 x^{4} - 23 x^{2} - 10 x) d x

(2 x + 5)^{2}

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