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

The solution to expand (2xe^x-2e^x)^2 is 4e^{2x}x^2-8e^{2x}x+4e^{2x}

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

expand

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

4 e^{2 x} x^{2} - 8 e^{2 x} x + 4 e^{2 x}

Solution steps

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

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

Apply Perfect Square Formula:

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

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

= (2 x e^{x})^{2} - 2 \cdot 2 x e^{x} \cdot 2 e^{x} + (2 e^{x})^{2}

Simplify

(2 x e^{x})^{2} - 2 \cdot 2 x e^{x} \cdot 2 e^{x} + (2 e^{x})^{2} : 4 e^{2 x} x^{2} - 8 e^{2 x} x + 4 e^{2 x}

= 4 e^{2 x} x^{2} - 8 e^{2 x} x + 4 e^{2 x}

(6 x^{4} - 5 x^{2} - 7) l e f t (- 4 x^{3})

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\frac{( s ^{3} - 3 s )}{( s ^{4} - 9 )}

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

What is expand (2xe^x-2e^x)^2 ?
The solution to expand (2xe^x-2e^x)^2 is 4e^{2x}x^2-8e^{2x}x+4e^{2x}