I have an expression of the following form (yet way longer)
(u^2 - Sqrt[z1])^2 (u^3 - Sqrt[z1])^3 (u^4 - Sqrt[z1])^2
(u^2 + Sqrt[z1])^2 (u^3 + Sqrt[z1])^3 (u^4 + Sqrt[z1])^2
(-1 + u^18 z1^(5/2)) (1 + u^18 z1^(5/2))
As you can see, terms combine by pairs to produce
(u^4 - z1)^2 (u^6 - z1)^2 (u^8-z1)^2 (-1 + u^36 z1^5)
Does there exist a command in Mathematica to do this simplification?
The full expression is this one:
(1 + u^4)^3 (1 - u^3 + u^6)^2 (1 + u^3 + u^6)^2 (1 - u^4 + u^8)^3
(-1 + u^12)^7 (1 - u^6 + u^12)^2 (u^2 - Sqrt[z1])^2 (u^3 - Sqrt[z1])^3
(u^4 - Sqrt[z1])^2 (u^9 - Sqrt[z1])^2 (u^12 - Sqrt[z1])^3
(u^18 - Sqrt[z1])^2 (u^2 + Sqrt[z1])^2 (u^3 + Sqrt[z1])^3
(u^4 + Sqrt[z1])^2 (u^9 + Sqrt[z1])^2 (u^12 + Sqrt[z1])^3
(u^18 + Sqrt[z1])^2 (-1 + u^2 Sqrt[z1])^2 (1 + u^2 Sqrt[z1])^2
(-1 + u^3 Sqrt[z1])^3 (1 + u^3 Sqrt[z1])^3 (-1 + u^4 Sqrt[z1])^2
(1 + u^4 Sqrt[z1])^2 (-1 + u^9 Sqrt[z1])^2 (1 + u^9 Sqrt[z1])^2
(-1 + u^12 Sqrt[z1])^3 (1 + u^12 Sqrt[z1])^3 (-1 + u^18 Sqrt[z1])^2
(1 + u^18 Sqrt[z1])^2 (u^3 - z1)^2 (u^9 - z1)^2 (-1 + z1)^5 (1 + z1)^2
(u^3 + z1)^2 (u^6 + z1)^3 (u^9 + z1)^2 (u^12 + z1)^3 (u^18 + z1)^2
(1 - Sqrt[z1] + z1)^2 (1 + Sqrt[z1] + z1)^2 (u^4 - u^2 Sqrt[z1] + z1)^2
(u^4 + u^2 Sqrt[z1] + z1)^2 (u^8 - u^4 Sqrt[z1] + z1)^2
(u^8 + u^4 Sqrt[z1] + z1)^2 (u^12 - u^6 Sqrt[z1] + z1)^2
(u^12 + u^6 Sqrt[z1] + z1)^2 (-1 + u^3 z1)^2 (1 + u^3 z1)^2
(1 - u^2 Sqrt[z1] + u^4 z1)^2 (1 + u^2 Sqrt[z1] + u^4 z1)^2
(1 + u^6 z1)^3 (1 - u^4 Sqrt[z1] + u^8 z1)^2
(1 + u^4 Sqrt[z1] + u^8 z1)^2 (-1 + u^9 z1)^2 (1 + u^9 z1)^2
(1 + u^12 z1)^3 (1 - u^6 Sqrt[z1] + u^12 z1)^2 (1 + u^6 Sqrt[z1] + u^12 z1)^2
(1 + u^18 z1)^2 (u^6 + z1^2)^2 (u^12 + z1^2) (u^18 + z1^2)^2
(1 + u^6 z1^2)^2 (1 + u^12 z1^2) (1 + u^18 z1^2)^2 (u^18 - z1^(5/2))
(u^18 + z1^(5/2)) (-1 + u^18 z1^(5/2)) (1 + u^18 z1^(5/2))
(z1 + u^24 z1 - u^12 (1 + z1^2))^6
and FullSimplify does not modify it.