Linear Algebra students might recognize this result from the topic “Partitioned Matrices”. Most (all?) intro linear algebra texts will have a section on this topic. Might be worth pointing out in the lab, as this will cue students that they may have seen this topic before.

General result (as long as dimensions align): [A|B] [C|D]^T = AC^T + B|D^T. (usually written w/o the transpose, but I would need math formatting to write [C|D]^T as a column vector).