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

The solution to expand (1+2e^x)^3 is 1+6e^x+12e^{2x}+8e^{3x}

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expand (1+2e^x)^3

expand

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

1 + 6 e^{x} + 12 e^{2 x} + 8 e^{3 x}

Solution steps

(1 + 2 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 = 2 e^{x}

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

Simplify

1^{3} + 3 \cdot 1^{2} \cdot 2 e^{x} + 3 \cdot 1 \cdot (2 e^{x})^{2} + (2 e^{x})^{3} : 1 + 6 e^{x} + 12 e^{2 x} + 8 e^{3 x}

= 1 + 6 e^{x} + 12 e^{2 x} + 8 e^{3 x}

(5 + 3 x 2) (3 x + 2)

(d g - x n)^{2}

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

- \frac{10 x + 13}{2 ( 3 x + 2 )}

(1 + cos (x))^{2} (tan (\frac{x}{2}))

What is expand (1+2e^x)^3 ?
The solution to expand (1+2e^x)^3 is 1+6e^x+12e^{2x}+8e^{3x}