1. ## Special Product

(ax+y)^2

normally i would answer it as :
(a^2)(x^2)+(y^2)

but with special products it would be:
(a^2)(x^2 ) + ( 2axy ) + ( y^2 )

does that mean

(a^2)(x^2)+(y^2)

is wrong?

2. ## Re: Special Product

What do you mean by special product?

does that mean
a2x2+y2
is wrong?
Yes. For any $u$ and $v$, $(u + v)^2 = u^2 + 2uv + v^2$. Here $u = ax$ and $v = y$; therefore, $(ax + y)^2 = a^2x^2+2axy+y^2$. You can check this by multiplying $(ax+y)(ax+y)$ through explicitly, and also by substituting various numbers for a, x and y (e.g., a = x = y = 1).