In mathematics, a product is the result of multiplication,

or Factoristion, ab+ac=a(b+c) <== a Product of a and (b+c)

I mean, I don’t like to argue about this

And yet here you are arguing with someone who is and is a Maths teacher

there is an implied multiplication there.

Nope! It's a Term/Product. There's no such thing as "implied multiplication" - you won't find it in any Maths textbook