In the paper linear forms in the logarithms of real algebraic numbers close to 1, it is written on page $9$ that-
$(xz)^k\leq b^3 \implies (a+1)(ab^2+1) \leq b^3$ , I could not figure it out. Here, $(xz)^k=(a+1)(ab^2+1)$ (see page $8$),$a, b \geq 2, $ and both are integers, $k\geq 3 $ (see theorem 11 on page $8$, please see the attached-paper for detail ).
If we simplify by Rearrangement inequality, we have that
how this could be less than or equal to $b^3$?