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

The solution to expand (2+e^x)^3 is 8+12e^x+6e^{2x}+e^{3x}

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expand (2+e^x)^3

expand

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

8 + 12 e^{x} + 6 e^{2 x} + e^{3 x}

Solution steps

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

Apply Perfect Cube Formula:

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

a = 2, b = e^{x}

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

Simplify

2^{3} + 3 \cdot 2^{2} e^{x} + 3 \cdot 2 (e^{x})^{2} + (e^{x})^{3} : 8 + 12 e^{x} + 6 e^{2 x} + e^{3 x}

= 8 + 12 e^{x} + 6 e^{2 x} + e^{3 x}

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What is expand (2+e^x)^3 ?
The solution to expand (2+e^x)^3 is 8+12e^x+6e^{2x}+e^{3x}