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

The solution to expand (3x+2e)^3 is 27x^3+54ex^2+36e^2x+8e^3

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expand (3x+2e)^3

expand

(3 x + 2 e)^{3}

27 x^{3} + 54 e x^{2} + 36 e^{2} x + 8 e^{3}

Solution steps

(3 x + 2 e)^{3}

Apply Perfect Cube Formula:

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

a = 3 x, b = 2 e

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

Simplify

(3 x)^{3} + 3 (3 x)^{2} \cdot 2 e + 3 \cdot 3 x (2 e)^{2} + (2 e)^{3} : 27 x^{3} + 54 e x^{2} + 36 e^{2} x + 8 e^{3}

= 27 x^{3} + 54 e x^{2} + 36 e^{2} x + 8 e^{3}

- e^{\frac{y x}{2}} csc^{2} (e^{\frac{y x}{2}}) (z x + y)

(x y + \frac{5}{8}) (\frac{3}{4} - x y)

\frac{( x - 3 ) ^{2}}{3}

12 (x - \frac{5}{2})^{2} + 70

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

What is expand (3x+2e)^3 ?
The solution to expand (3x+2e)^3 is 27x^3+54ex^2+36e^2x+8e^3