All functions can be written as sum of product of $x$ and $y$?

Question

Can all functions of two variables ($x$ and $y$) be written as the sum of the products of a function of $x$ and a function of $y$? E.g.

$a(x,y) = f(x)g(y) + h(x)i(y) + j(x)k(y) ...$

Answer 1

Let consider as counterexample $$f(x,y)=\log (x+y)$$