# identify notable (special) binomial products

I've been ask in homework to identify, among others, the following special binomial products:

$(6x-2y)(2x-6y)$

$(x+3y)(7x^9+4)$

$(a^2b+c)(ac+b)$

I've been taught only 4 special binomial products

$(x\pm y)^2$

$(x\pm y)^3$

$(x-y)(x+y)$

$(x+a)(x+b)$ common term

None of the three first products I wrote seem to be one of this 4, is there any special products I'm missing?

• Just do the multiplications. Don't worry about those "special" products. If you can't use them, you can't use them, and you should move on to straight-forward calculations. – Arthur Jul 7 '16 at 7:23
• What do you mean by "identify"? What exactly are you asked to do? Are you sure you are not simply asked to expand the expressions, eg to get $12x^2-40xy+12y^2$ for the first one? – almagest Jul 7 '16 at 7:42
• I was asked to identify and also expand the product, for instance the first one was $(2x-3)(2x+3)$ which is easily seen to be of the form $(x-y)(x+y)=x^2-y^2$ then its expansion is $4x^2-9$, by identify I mean I have to say "this is two binomials that are conjugates". (I'm not an english speaker so I'm not sure this what you call it but they do have a name) We're following a book made by the math department and the homework comes from that book. So probably in those cases all I have to do is expand. – Novato Jul 7 '16 at 8:01