Mister Exam

Factor polynomial x^6-y^4

An expression to simplify:

The solution

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