It’s a trick question, the two expressions are exactly equivalent!

I constructed this myself and then went looking for other examples, but struggled to find any others.

The way I stumbled across this was to try to find a simpler expression for the product of pairwise sums of three numbers:

(a+b)(a+c)(b+c)

I reasoned that each of those sums could be thought of as the sum of all three numbers less one of them. If I call the sum of all three ‘s’ it becomes:

(s-c)(s-b)(s-a)

Multiplying this out I get:

s^3 – (a+b+c)s^2 + (ab+ac+bc)s – abc

However since (a+b+c) is equal to s, the first two terms cancel each other and we find that:

(a+b)(a+c)(b+c)=(ab+ac+bc)(a+b+c)-abc

Adding abc to each side and we get an equation demonstrating the equivalence of the two expressions we started with, which have to beautiful property of interchanging the multiplications and additions.

(a+b)(a+c)(b+c)+abc=(ab+ac+bc)(a+b+c)