What is (2n-insqrt(12))^3 ?

The solution to (2n-insqrt(12))^3 is -64n^3

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simplify (2n-insqrt(12))^3

simplify

(2 n - in 12)^{3}

- 64 n^{3}

Solution steps

(2 n - in 12)^{3}

Rewrite

2 n - in 12

in standard complex form:

2 n - n 12 i

= (2 n - n 12 i)^{3}

12 = 23

= (2 n - n \cdot 23 i)^{3}

Apply Perfect Cube Formula:

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

(2 n - n \cdot 23 i)^{3} = (2 n)^{3} - 3 (2 n)^{2} n \cdot 23 i + 3 \cdot 2 n (n \cdot 23 i)^{2} - (n \cdot 23 i)^{3}

= (2 n)^{3} - 3 (2 n)^{2} n \cdot 23 i + 3 \cdot 2 n (n \cdot 23 i)^{2} - (n \cdot 23 i)^{3}

Simplify

(2 n)^{3} - 3 (2 n)^{2} n \cdot 23 i + 3 \cdot 2 n (n \cdot 23 i)^{2} - (n \cdot 23 i)^{3} : - 64 n^{3}

= - 64 n^{3}

+ 13 y^{2} - 5 y x - 8 x^{2}

\frac{1}{x + 1 + x}

\frac{5}{3} \times 6

4 x^{18}