i really dont see this question matching with any of the identities

(a^2 + b^2) (-a^2 + b^2)

$$(a^2 + b^2) (-a^2 + b^2)\\\\
=(b^2 + a^2) (b^2 -a^2)\\\\$$

Now you can see that it is  the difference of 2 squares. :)

so the answer is 

$$\\=(b^2)^2-(a^2)^2\\\\
=b^4-a^4$$

Does that all makes sense Rosala ?     

umm no...not to me right now!

how did you  just swap everything ......i dont get it!

{i am talking about this step}(b^2 + a^2) (b^2 -a^2)

its like sorting out a ball  of wool!

Okay rosala let's look at this.

a+b=b+a              agreed?     (1)

a-b=-b+a              agreed?     (2)

-b+a=a-b              agreed? (It is the same as the one above only in reverse)    (3)

so

$${{\mathtt{a}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{b}}}^{{\mathtt{2}}} = {{\mathtt{b}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{a}}}^{{\mathtt{2}}}$$            agreed?  (4)

and

$${\mathtt{\,-\,}}{{\mathtt{a}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{b}}}^{{\mathtt{2}}} = {{\mathtt{b}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{{\mathtt{a}}}^{{\mathtt{2}}}$$         agreed ?  (5)

so

$$(a^2 + b^2) (-a^2 + b^2)=(b^2 + a^2) (b^2 -a^2)\\\\$$       agreed  (6)

I have numbered all the lines so that you can tell me which ones don't make sense to you.  :)

All of them make sense to me Melody!Than you very much!

Good - I am glad i could help :)