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Expression simplification/ Factorization polynomials/ y^16-1

Factor polynomial y^16-1

An expression to simplify:

The solution

You have entered [src] 
 16    
y   - 1
y16−1y^{16} - 1 
y^16 - 1
Factorization [src] 
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(x + 1)*(x - 1)*(x + I)*(x - I)*|x + ----- + -------|*|x + ----- - -------|*|x + - ----- + -------|*|x + - ----- - -------|*|x +   /   - - -----  + I*  /   - + ----- |*|x +   /   - - -----  - I*  /   - + ----- |*|x + -   /   - - -----  + I*  /   - + ----- |*|x + -   /   - - -----  - I*  /   - + ----- |*|x +   /   - + -----  + I*  /   - - ----- |*|x +   /   - + -----  - I*  /   - - ----- |*|x + -   /   - + -----  + I*  /   - - ----- |*|x + -   /   - + -----  - I*  /   - - ----- |
                                \      2        2   / \      2        2   / \        2        2   / \        2        2   / \    \/    2     4        \/    2     4   / \    \/    2     4        \/    2     4   / \      \/    2     4        \/    2     4   / \      \/    2     4        \/    2     4   / \    \/    2     4        \/    2     4   / \    \/    2     4        \/    2     4   / \      \/    2     4        \/    2     4   / \      \/    2     4        \/    2     4   /
(x−1)(x+1)(x+i)(x−i)(x+(22+2i2))(x+(22−2i2))(x+(−22+2i2))(x+(−22−2i2))(x+(12−24+i24+12))(x+(12−24−i24+12))(x+(−12−24+i24+12))(x+(−12−24−i24+12))(x+(24+12+i12−24))(x+(24+12−i12−24))(x+(−24+12+i12−24))(x+(−24+12−i12−24))\left(x - 1\right) \left(x + 1\right) \left(x + i\right) \left(x - i\right) \left(x + \left(\frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)\right) \left(x + \left(\frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)\right) \left(x + \left(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)\right) \left(x + \left(- \frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)\right) \left(x + \left(\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} + i \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}\right)\right) \left(x + \left(\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} - i \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}\right)\right) \left(x + \left(- \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} + i \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}\right)\right) \left(x + \left(- \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} - i \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}\right)\right) \left(x + \left(\sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}} + i \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}\right)\right) \left(x + \left(\sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}} - i \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}\right)\right) \left(x + \left(- \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}} + i \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}\right)\right) \left(x + \left(- \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}} - i \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}\right)\right) 
(((((((((((((((x + 1)*(x - 1))*(x + i))*(x - i))*(x + sqrt(2)/2 + i*sqrt(2)/2))*(x + sqrt(2)/2 - i*sqrt(2)/2))*(x - sqrt(2)/2 + i*sqrt(2)/2))*(x - sqrt(2)/2 - i*sqrt(2)/2))*(x + sqrt(1/2 - sqrt(2)/4) + i*sqrt(1/2 + sqrt(2)/4)))*(x + sqrt(1/2 - sqrt(2)/4) - i*sqrt(1/2 + sqrt(2)/4)))*(x - sqrt(1/2 - sqrt(2)/4) + i*sqrt(1/2 + sqrt(2)/4)))*(x - sqrt(1/2 - sqrt(2)/4) - i*sqrt(1/2 + sqrt(2)/4)))*(x + sqrt(1/2 + sqrt(2)/4) + i*sqrt(1/2 - sqrt(2)/4)))*(x + sqrt(1/2 + sqrt(2)/4) - i*sqrt(1/2 - sqrt(2)/4)))*(x - sqrt(1/2 + sqrt(2)/4) + i*sqrt(1/2 - sqrt(2)/4)))*(x - sqrt(1/2 + sqrt(2)/4) - i*sqrt(1/2 - sqrt(2)/4))
Numerical answer [src] 
-1.0 + y^16
-1.0 + y^16
Combinatorics [src] 
        /     2\ /     4\ /     8\         
(1 + y)*\1 + y /*\1 + y /*\1 + y /*(-1 + y)
(y−1)(y+1)(y2+1)(y4+1)(y8+1)\left(y - 1\right) \left(y + 1\right) \left(y^{2} + 1\right) \left(y^{4} + 1\right) \left(y^{8} + 1\right) 
(1 + y)*(1 + y^2)*(1 + y^4)*(1 + y^8)*(-1 + y)
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