What is expand (e^{2x}+1)^3 ?

The solution to expand (e^{2x}+1)^3 is e^{6x}+3e^{4x}+3e^{2x}+1

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expand (e^{2x}+1)^3

expand

(e^{2 x} + 1)^{3}

e^{6 x} + 3 e^{4 x} + 3 e^{2 x} + 1

Solution steps

(e^{2 x} + 1)^{3}

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

a = e^{2 x}, b = 1

= (e^{2 x})^{3} + 3 (e^{2 x})^{2} \cdot 1 + 3 e^{2 x} \cdot 1^{2} + 1^{3}

Simplify

(e^{2 x})^{3} + 3 (e^{2 x})^{2} \cdot 1 + 3 e^{2 x} \cdot 1^{2} + 1^{3} : e^{6 x} + 3 e^{4 x} + 3 e^{2 x} + 1

= e^{6 x} + 3 e^{4 x} + 3 e^{2 x} + 1

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What is expand (e^{2x}+1)^3 ?
The solution to expand (e^{2x}+1)^3 is e^{6x}+3e^{4x}+3e^{2x}+1