Finding by what factor two operators differ

[H.fulls]

Homework Statement

I have two operators
$\hat{A}^{2}$$\hat{B}^{2}$+$\hat{B}^{2}$$\hat{A}^{2}$

1/2($\hat{A}$$\hat{B}$+$\hat{B}$$\hat{A}$) $^{2}$

By what factor do the two operators differ?

The Attempt at a Solution

I believe I either have to find the inner products of them and relate them somehow or use commutation?
Not sure which one!
I don't want help with the maths as I really need to try figure that bit out myself! But I am not quite sure what the question is asking me to do.

 

[andrien]

try commutation,if given.