8(x⁴+7x²y²-10y⁴)= (this is as far as it goes for rational factorisation)
8(x⁴+7x²y²+49y⁴/4-49y⁴/4-10y⁴)=
8((x²+7y²/2)²-y⁴(49/4+10))=
8(x²+7y²/2+y²√89/2)(x²+7y²/2-y²√89/2).
Further factorisation is possible for x²+7y²/2-y²√89/2, but more irrational terms are introduced.
[If the original expression had been 8x⁴+56x²y²+10y⁴, it would factorise:
8(x²+5y²)(x²+2y²).]