Разложить многочлен на множители -1600+a^12

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$$\left(a - \sqrt{2} \cdot \sqrt[6]{5}\right) 1 \left(a + \sqrt{2} \cdot \sqrt[6]{5}\right) \left(a + \sqrt{2} \cdot \sqrt[6]{5} i\right) \left(a - \sqrt{2} \cdot \sqrt[6]{5} i\right) \left(a + \left(\frac{\sqrt{2} \cdot \sqrt[6]{5}}{2} + \frac{\sqrt[6]{5} \sqrt{6} i}{2}\right)\right) \left(a + \left(\frac{\sqrt{2} \cdot \sqrt[6]{5}}{2} - \frac{\sqrt[6]{5} \sqrt{6} i}{2}\right)\right) \left(a - \left(\frac{\sqrt{2} \cdot \sqrt[6]{5}}{2} - \frac{\sqrt[6]{5} \sqrt{6} i}{2}\right)\right) \left(a - \left(\frac{\sqrt{2} \cdot \sqrt[6]{5}}{2} + \frac{\sqrt[6]{5} \sqrt{6} i}{2}\right)\right) \left(a + \left(\frac{\sqrt[6]{5} \sqrt{6}}{2} + \frac{\sqrt{2} \cdot \sqrt[6]{5} i}{2}\right)\right) \left(a + \left(\frac{\sqrt[6]{5} \sqrt{6}}{2} - \frac{\sqrt{2} \cdot \sqrt[6]{5} i}{2}\right)\right) \left(a - \left(\frac{\sqrt[6]{5} \sqrt{6}}{2} - \frac{\sqrt{2} \cdot \sqrt[6]{5} i}{2}\right)\right) \left(a - \left(\frac{\sqrt[6]{5} \sqrt{6}}{2} + \frac{\sqrt{2} \cdot \sqrt[6]{5} i}{2}\right)\right)$$

(((((((((((1*(a + sqrt(2)*5^(1/6)))*(a - sqrt(2)*5^(1/6)))*(a + i*sqrt(2)*5^(1/6)))*(a - i*sqrt(2)*5^(1/6)))*(a + (sqrt(2)*5^(1/6)/2 + i*5^(1/6)*sqrt(6)/2)))*(a + (sqrt(2)*5^(1/6)/2 - i*5^(1/6)*sqrt(6)/2)))*(a - (sqrt(2)*5^(1/6)/2 + i*5^(1/6)*sqrt(6)/2)))*(a - (sqrt(2)*5^(1/6)/2 - i*5^(1/6)*sqrt(6)/2)))*(a + (5^(1/6)*sqrt(6)/2 + i*sqrt(2)*5^(1/6)/2)))*(a + (5^(1/6)*sqrt(6)/2 - i*sqrt(2)*5^(1/6)/2)))*(a - (5^(1/6)*sqrt(6)/2 + i*sqrt(2)*5^(1/6)/2)))*(a - (5^(1/6)*sqrt(6)/2 - i*sqrt(2)*5^(1/6)/2))