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Expression simplification/ Factorization polynomials/ x^8-4

Factor polynomial x^8-4

An expression to simplify:

The solution

You have entered [src] 
 8    
x  - 4
$$x^{8} - 4$$ 
x^8 - 4
Factorization [src] 
                                                    /     3/4      3/4\ /     3/4      3/4\ /       3/4      3/4\ /       3/4      3/4\
/    4 ___\ /    4 ___\ /      4 ___\ /      4 ___\ |    2      I*2   | |    2      I*2   | |      2      I*2   | |      2      I*2   |
\x + \/ 2 /*\x - \/ 2 /*\x + I*\/ 2 /*\x - I*\/ 2 /*|x + ---- + ------|*|x + ---- - ------|*|x + - ---- + ------|*|x + - ---- - ------|
                                                    \     2       2   / \     2       2   / \       2       2   / \       2       2   /
$$\left(x - \sqrt[4]{2}\right) \left(x + \sqrt[4]{2}\right) \left(x + \sqrt[4]{2} i\right) \left(x - \sqrt[4]{2} i\right) \left(x + \left(\frac{2^{\frac{3}{4}}}{2} + \frac{2^{\frac{3}{4}} i}{2}\right)\right) \left(x + \left(\frac{2^{\frac{3}{4}}}{2} - \frac{2^{\frac{3}{4}} i}{2}\right)\right) \left(x + \left(- \frac{2^{\frac{3}{4}}}{2} + \frac{2^{\frac{3}{4}} i}{2}\right)\right) \left(x + \left(- \frac{2^{\frac{3}{4}}}{2} - \frac{2^{\frac{3}{4}} i}{2}\right)\right)$$ 
(((((((x + 2^(1/4))*(x - 2^(1/4)))*(x + i*2^(1/4)))*(x - i*2^(1/4)))*(x + 2^(3/4)/2 + i*2^(3/4)/2))*(x + 2^(3/4)/2 - i*2^(3/4)/2))*(x - 2^(3/4)/2 + i*2^(3/4)/2))*(x - 2^(3/4)/2 - i*2^(3/4)/2)
Numerical answer [src] 
-4.0 + x^8
-4.0 + x^8
Combinatorics [src] 
/      4\ /     4\
\-2 + x /*\2 + x /
$$\left(x^{4} - 2\right) \left(x^{4} + 2\right)$$ 
(-2 + x^4)*(2 + x^4)
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