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

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

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

expand

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

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

Solution steps

(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 e^{2 x} x

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

Simplify

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

\frac{7 ( 3 a - 1 )}{b ( 5 a + 1 )}

4 (0.5 f - 0.25 = 6 + f)

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

- \frac{4}{( x - 1 ) ^{2}}

\frac{( R ^{2} C s + 2 R ) C s}{RC s + 1} - 1 - RC s

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