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

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

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expand (1+e^x)^3

expand

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

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

Solution steps

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

Apply Perfect Cube Formula:

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

a = 1, b = e^{x}

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

Simplify

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

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

(6 x y - 2 y^{2} + 1) d x

\frac{d}{d y} ((x) (cos (x) y + 3 x y^{2}))

(- 43 + 4 i)^{5}

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

\frac{1}{12} (cos (8 t) - 8 sin (8 t))

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