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

The solution to expand (2e^{3x}+1)^3 is 8e^{9x}+12e^{6x}+6e^{3x}+1

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

expand

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

8 e^{9 x} + 12 e^{6 x} + 6 e^{3 x} + 1

Solution steps

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

Apply Perfect Cube Formula:

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

a = 2 e^{3 x}, b = 1

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

Simplify

(2 e^{3 x})^{3} + 3 (2 e^{3 x})^{2} \cdot 1 + 3 \cdot 2 e^{3 x} \cdot 1^{2} + 1^{3} : 8 e^{9 x} + 12 e^{6 x} + 6 e^{3 x} + 1

= 8 e^{9 x} + 12 e^{6 x} + 6 e^{3 x} + 1

\frac{3}{4} (16 x - 12)

(- 1 - \frac{1}{jk r}) (- 1 + \frac{1}{jk r})

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

(x + i \cdot y)^{3}

(3, 1, 2) (2, 3, 7) y (1, - 3, 8)

What is expand (2e^{3x}+1)^3 ?
The solution to expand (2e^{3x}+1)^3 is 8e^{9x}+12e^{6x}+6e^{3x}+1