Well, that last answer is not correct. I hope no children read it. In a binomial expansion, the coefficients are given by pascal's triangle.

So (a+b)^7 = a^7 + 7a^6b+ 21a^5b^2 + 35a^4b^3 + 35a^3b^4 + 21a^2b^5 + 7ab^6 +b^7

So (a+b)^7 -a^7 - b^7 = 7ab(a^5+ 3a^4b + 5a^3b^2 + 5a^2b^3 + 3ab^4 + b^5)

I leave it to others to take it from here

*Edited on ***June 7, 2015, 7:39 pm**