Mister Exam

# Factor polynomial x^8-y^6

An expression to simplify:

### The solution

You have entered [src]
 8    6
x  - y 
$$x^{8} - y^{6}$$
x^8 - y^6
Factorization [src]
                                /             ____              ____\ /             ____              ____\ /               ____              ____\ /               ____              ____\
/         ____\ /         ____\ |      ___ 8 /  6        ___ 8 /  6 | |      ___ 8 /  6        ___ 8 /  6 | |        ___ 8 /  6        ___ 8 /  6 | |        ___ 8 /  6        ___ 8 /  6 | /       ____\ /       ____\
|      8 /  6 | |      8 /  6 | |    \/ 2 *\/  y     I*\/ 2 *\/  y  | |    \/ 2 *\/  y     I*\/ 2 *\/  y  | |      \/ 2 *\/  y     I*\/ 2 *\/  y  | |      \/ 2 *\/  y     I*\/ 2 *\/  y  | |    8 /  6 | |    8 /  6 |
\x + I*\/  y  /*\x - I*\/  y  /*|x + ------------- + ---------------|*|x + ------------- - ---------------|*|x + - ------------- + ---------------|*|x + - ------------- - ---------------|*\x + \/  y  /*\x - \/  y  /
\          2                2       / \          2                2       / \            2                2       / \            2                2       /                            
$$\left(x - i \sqrt[8]{y^{6}}\right) \left(x + i \sqrt[8]{y^{6}}\right) \left(x + \left(\frac{\sqrt{2} \sqrt[8]{y^{6}}}{2} + \frac{\sqrt{2} i \sqrt[8]{y^{6}}}{2}\right)\right) \left(x + \left(\frac{\sqrt{2} \sqrt[8]{y^{6}}}{2} - \frac{\sqrt{2} i \sqrt[8]{y^{6}}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{2} \sqrt[8]{y^{6}}}{2} + \frac{\sqrt{2} i \sqrt[8]{y^{6}}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{2} \sqrt[8]{y^{6}}}{2} - \frac{\sqrt{2} i \sqrt[8]{y^{6}}}{2}\right)\right) \left(x + \sqrt[8]{y^{6}}\right) \left(x - \sqrt[8]{y^{6}}\right)$$
(((((((x + i*(y^6)^(1/8))*(x - i*(y^6)^(1/8)))*(x + sqrt(2)*(y^6)^(1/8)/2 + i*sqrt(2)*(y^6)^(1/8)/2))*(x + sqrt(2)*(y^6)^(1/8)/2 - i*sqrt(2)*(y^6)^(1/8)/2))*(x - sqrt(2)*(y^6)^(1/8)/2 + i*sqrt(2)*(y^6)^(1/8)/2))*(x - sqrt(2)*(y^6)^(1/8)/2 - i*sqrt(2)*(y^6)^(1/8)/2))*(x + (y^6)^(1/8)))*(x - (y^6)^(1/8))
Combinatorics [src]
/ 4    3\ / 4    3\
\x  + y /*\x  - y /
$$\left(x^{4} - y^{3}\right) \left(x^{4} + y^{3}\right)$$
(x^4 + y^3)*(x^4 - y^3)
x^8 - y^6
x^8 - y^6