Prove or disprove $(A+B)^p ≤ p(A^p + B^p)$

[twoflower]

I've encountered this nice-looking inequality:

$$\left(A+B\right)^{p} \le p\left(A^{p}+B^{p}\right)$$

(p can irrational as well)

but I can't find a way to prove or disprove its correctness. I've tried using the binomial theorem, but it didn't seem it would lead me to the finish.

Could someone please tell me how to prove that?

Thank you very much!

 

[Dick]

Yeah, looks nice. But there must be other premises. Taking A=0 shows you need p>=1. e.g.

 

[drpizza]

What other info do you have?
For example, (2+3)^3 <= 3(2^3 + 3^3)
Nope, doesn't work.

(0 + 1)^(power) isn't going to be less than that power*(0^power + 1^power)

So, there must be some restriction on A, B, and p that you haven't stated.