Algebra inequality question

[uneven dragon]

I really suck with this types of 'to prove' questions, specially the ones with inequalities, someone please help!

[sullen imp]

Do the expansion of (a + b)4 , I don't know whether it works but yeah

It probably will

[plush echo]

Is the question resolved?

[tepid totem]

@uneven dragon Firstly, are a and b non zero natural numbers?

Try to prove that a4 + b4 - a3b - ab3 > 0 by factorising the left part of this inequality.

[formal brook]

Observing the binomial expansion of (a - b)^4 might be good approach for this proof.

[brave plinth]

just do it with derivatives

[mild garden]

Trivial by muirheads inequality

[delicate vigil]

With a=b the inequality does not hold.