1. The problem statement, all variables and given/known data For a,b,c,d >1, Show that (a+1)(b+1)(c+1)(d+1) < 8(abcd+1) 2. Relevant equations How to show this? 3. The attempt at a solution I could show for two variables, (a+1)(b+1)<2(ab+1). Tried C-S, AM-GM inequalities in different form and variable transformations. But still no result. It's my daughters test question. Any help is appreciated.