Once you have proved a2 − b2 = (a + b)(a − b), you have also proved p2 − q2 = (p + q)(p − q). If a syllogism is valid, you can substitute other terms in it and it will still be valid.
In related news, Dale Carrico wrote:
IV. To declare that money is speech is to ensure that only money talks.It makes just as much (or as little) sense to say:
IVa. To declare that print is speech is to ensure that only print talks.I won't more than mention the fact that, according to VI, I do not exist or that XLII sounded familiar.