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Popular >

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

Solution

expand

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

Solution

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

Solution steps

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

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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