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

The solution to expand (e^{2x}+xe^{2x})^2 is e^{4x}+2e^{4x}x+e^{4x}x^2

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

expand

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

e^{4 x} + 2 e^{4 x} x + e^{4 x} x^{2}

Solution steps

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

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

Apply Perfect Square Formula:

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

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

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

Simplify

(e^{2 x})^{2} + 2 e^{2 x} x e^{2 x} + (x e^{2 x})^{2} : e^{4 x} + 2 e^{4 x} x + e^{4 x} x^{2}

= e^{4 x} + 2 e^{4 x} x + e^{4 x} x^{2}

\frac{3 s + 4}{3 ( s + 2 ) ( s + 1 )}

\frac{9 s ^{2} + 384}{2 s ( s ^{2} + 64 )}

(7 - x - 2)^{2}

5 (3 - 5)

4 a^{2} (\frac{π}{2} - 1)

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