56-22x8,
2(28-11x8) is the only rational factorisation. Any further simplification (through factorisation) produces irrational factors, some of which are complex (involving the imaginary square root of -1).
28 and 11 have irrational eighth roots.
An expression of the type ab8-ax8 factorises:
a(b-x)(b7+b6x+b5x2+b4x3+b3x4+b2x5+bx6+x7).
It also factorises:
a(b8-x8),
a(b4+x4)(b4-x4),
a(b4+x4)(b2+x2)(b2-x2),
a(b4+x4)(b2+x2)(b+x)(b-x).
So if a(b8-x8)≡56-22x8, then ab8≡56 and ax8≡22x8⇒
a=22, b8=56/a=56/22=28/11; b=8√(28/11)=1.12388 approx (irrational).
a(b8-x8)≡22(28/11-x8).
Substituting for a and b in the above factorisations will produce the "simplifications".