What is expand (e^{2x}+e^{3x})^2 ?

The solution to expand (e^{2x}+e^{3x})^2 is e^{4x}+2e^{5x}+e^{6x}

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expand (e^{2x}+e^{3x})^2

expand

(e^{2 x} + e^{3 x})^{2}

e^{4 x} + 2 e^{5 x} + e^{6 x}

Solution steps

(e^{2 x} + e^{3 x})^{2}

Apply Perfect Square Formula:

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

a = e^{2 x}, b = e^{3 x}

= (e^{2 x})^{2} + 2 e^{2 x} e^{3 x} + (e^{3 x})^{2}

Simplify

(e^{2 x})^{2} + 2 e^{2 x} e^{3 x} + (e^{3 x})^{2} : e^{4 x} + 2 e^{5 x} + e^{6 x}

= e^{4 x} + 2 e^{5 x} + e^{6 x}

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

(x + 4) (2 x + 3)

\frac{1}{( x + 8 ) ^{2}}

x^{2} (x + 3) e^{x}

(\frac{85 a}{5} + \frac{13 b}{3})^{2}

What is expand (e^{2x}+e^{3x})^2 ?
The solution to expand (e^{2x}+e^{3x})^2 is e^{4x}+2e^{5x}+e^{6x}