  We show that any $2$-coloring of $\mathbb{N}$ contains infinitely many
monochromatic sets of the form $\{x,y,xy,x+y\},$ and more generally
monochromatic sets of the form $\{x_i,\prod x_i,\sum x_i: i\leq k\}$ for any
$k\in\mathbb{N}.$ Along the way we prove a monochromatic products of sums
theorem that extends Hindman's theorem and a colorful variant of this result
that holds in any 'balanced' coloring.
