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

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

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

expand

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

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

Solution steps

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

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

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

Simplify

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

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

\frac{2 ( 2 e - 1 )}{3 e}

\frac{- 2 a ^{2} - 2 ab - b + 2}{( a - 1 ) ( - 4 - 2 a )}

\frac{a ^{2} ( 1 - e ^{a} )}{a ^{2} + 9 π ^{2}}

\frac{( x + 1 ) ^{2}}{( x ^{2} + 1 ) ^{3}}

f, f = e^{x} δ (x - 1)

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