Can someone please explain to me how A*-B and B*A become additive inverses?

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When you multiply them out, you get -ab and +ab. If you add those, you get 0. That's the definition of additive inverses... the +and- of the same number added together to get 0. Just like 6 and -6 or 35 and -35 are additive inverses. Basically, when you FOIL this out you get: a^2 + ab - ab - b^2 Combine like terms in the middle to get: a^2 + 0 - b^2, or just... a^2 - b^2. That's where the special case she gave is derived from.

bpeters is right!! thats how you would do it and figure it out!! and the F.O.I.L. means: F = first O = outer  I  = inner  L = last * just a reminder!! * GOOD LUCK!!

oh to answer your question, Additive Inverses just mean numbers that are opposite from each other, such as +6 and -6. If you add A*-b and B*A, you get 0 :).