Общий множитель -27-a^12

Комбинаторика

 /     4\ /     4      2\ /     4      2\
-\3 + a /*\3 + a  - 3*a /*\3 + a  + 3*a /

$$- \left(a^{4} + 3\right) \left(a^{4} - 3 a^{2} + 3\right) \left(a^{4} + 3 a^{2} + 3\right)$$

Разложение на множители

/      ___ 4 ___       ___ 4 ___\ /      ___ 4 ___       ___ 4 ___\ /        ___ 4 ___       ___ 4 ___\ /        ___ 4 ___       ___ 4 ___\ /      ___ 4 ___     ___  3/4       ___ 4 ___       ___  3/4\ /      ___ 4 ___     ___  3/4       ___ 4 ___       ___  3/4\ /        ___ 4 ___     ___  3/4       ___ 4 ___       ___  3/4\ /        ___ 4 ___     ___  3/4       ___  3/4       ___ 4 ___\ /      ___ 4 ___     ___  3/4       ___ 4 ___       ___  3/4\ /      ___ 4 ___     ___  3/4       ___  3/4       ___ 4 ___\ /      ___  3/4     ___ 4 ___       ___ 4 ___       ___  3/4\ /      ___  3/4     ___ 4 ___       ___ 4 ___       ___  3/4\
|    \/ 2 *\/ 3    I*\/ 2 *\/ 3 | |    \/ 2 *\/ 3    I*\/ 2 *\/ 3 | |      \/ 2 *\/ 3    I*\/ 2 *\/ 3 | |      \/ 2 *\/ 3    I*\/ 2 *\/ 3 | |    \/ 2 *\/ 3    \/ 2 *3      I*\/ 2 *\/ 3    I*\/ 2 *3   | |    \/ 2 *\/ 3    \/ 2 *3      I*\/ 2 *\/ 3    I*\/ 2 *3   | |      \/ 2 *\/ 3    \/ 2 *3      I*\/ 2 *\/ 3    I*\/ 2 *3   | |      \/ 2 *\/ 3    \/ 2 *3      I*\/ 2 *3      I*\/ 2 *\/ 3 | |    \/ 2 *\/ 3    \/ 2 *3      I*\/ 2 *\/ 3    I*\/ 2 *3   | |    \/ 2 *\/ 3    \/ 2 *3      I*\/ 2 *3      I*\/ 2 *\/ 3 | |    \/ 2 *3      \/ 2 *\/ 3    I*\/ 2 *\/ 3    I*\/ 2 *3   | |    \/ 2 *3      \/ 2 *\/ 3    I*\/ 2 *\/ 3    I*\/ 2 *3   |
|a + ----------- + -------------|*|a + ----------- - -------------|*|a + - ----------- + -------------|*|a + - ----------- - -------------|*|a + ----------- - ---------- - ------------- - ------------|*|a + ----------- - ---------- + ------------- + ------------|*|a + - ----------- - ---------- + ------------- - ------------|*|a + - ----------- - ---------- + ------------ - -------------|*|a + ----------- + ---------- + ------------- - ------------|*|a + ----------- + ---------- + ------------ - -------------|*|a + ---------- - ----------- - ------------- - ------------|*|a + ---------- - ----------- + ------------- + ------------|
\         2              2      / \         2              2      / \           2              2      / \           2              2      / \         4            4              4              4      / \         4            4              4              4      / \           4            4              4              4      / \           4            4             4               4      / \         4            4              4              4      / \         4            4             4               4      / \        4             4              4              4      / \        4             4              4              4      /

$$\left(a + \left(\frac{\sqrt{2} \sqrt[4]{3}}{2} - \frac{\sqrt{2} \sqrt[4]{3} i}{2}\right)\right) \left(a + \left(\frac{\sqrt{2} \sqrt[4]{3}}{2} + \frac{\sqrt{2} \sqrt[4]{3} i}{2}\right)\right) \left(a + \left(- \frac{\sqrt{2} \sqrt[4]{3}}{2} + \frac{\sqrt{2} \sqrt[4]{3} i}{2}\right)\right) \left(a + \left(- \frac{\sqrt{2} \sqrt[4]{3}}{2} - \frac{\sqrt{2} \sqrt[4]{3} i}{2}\right)\right) \left(a + \left(- \frac{\sqrt{2} \cdot 3^{\frac{3}{4}}}{4} + \frac{\sqrt{2} \sqrt[4]{3}}{4} - \frac{\sqrt{2} \cdot 3^{\frac{3}{4}} i}{4} - \frac{\sqrt{2} \sqrt[4]{3} i}{4}\right)\right) \left(a + \left(- \frac{\sqrt{2} \cdot 3^{\frac{3}{4}}}{4} + \frac{\sqrt{2} \sqrt[4]{3}}{4} + \frac{\sqrt{2} \sqrt[4]{3} i}{4} + \frac{\sqrt{2} \cdot 3^{\frac{3}{4}} i}{4}\right)\right) \left(a + \left(- \frac{\sqrt{2} \cdot 3^{\frac{3}{4}}}{4} - \frac{\sqrt{2} \sqrt[4]{3}}{4} - \frac{\sqrt{2} \cdot 3^{\frac{3}{4}} i}{4} + \frac{\sqrt{2} \sqrt[4]{3} i}{4}\right)\right) \left(a + \left(- \frac{\sqrt{2} \cdot 3^{\frac{3}{4}}}{4} - \frac{\sqrt{2} \sqrt[4]{3}}{4} - \frac{\sqrt{2} \sqrt[4]{3} i}{4} + \frac{\sqrt{2} \cdot 3^{\frac{3}{4}} i}{4}\right)\right) \left(a + \left(\frac{\sqrt{2} \sqrt[4]{3}}{4} + \frac{\sqrt{2} \cdot 3^{\frac{3}{4}}}{4} - \frac{\sqrt{2} \cdot 3^{\frac{3}{4}} i}{4} + \frac{\sqrt{2} \sqrt[4]{3} i}{4}\right)\right) \left(a + \left(\frac{\sqrt{2} \sqrt[4]{3}}{4} + \frac{\sqrt{2} \cdot 3^{\frac{3}{4}}}{4} - \frac{\sqrt{2} \sqrt[4]{3} i}{4} + \frac{\sqrt{2} \cdot 3^{\frac{3}{4}} i}{4}\right)\right) \left(a + \left(- \frac{\sqrt{2} \sqrt[4]{3}}{4} + \frac{\sqrt{2} \cdot 3^{\frac{3}{4}}}{4} - \frac{\sqrt{2} \cdot 3^{\frac{3}{4}} i}{4} - \frac{\sqrt{2} \sqrt[4]{3} i}{4}\right)\right) \left(a + \left(- \frac{\sqrt{2} \sqrt[4]{3}}{4} + \frac{\sqrt{2} \cdot 3^{\frac{3}{4}}}{4} + \frac{\sqrt{2} \sqrt[4]{3} i}{4} + \frac{\sqrt{2} \cdot 3^{\frac{3}{4}} i}{4}\right)\right)$$