Equation - what first? I have this equation:
$$
  (x+y)(x^x + y^y) = 2009.
$$
I must designate all pairs of integers satisfying the equation.
What first? I tried multiply brackets , but to no avail

hint: $2009=7^2\times 41$ so keeping in mind that $x+y\lt x^x+y^y$ we're looking for integers $x$ and $y$ such that
$$(x+y)(x^x+y^y)=7^2\times 41$$
This means finding integers such that $x+y=41$ and $x^x+y^y=49$ or $x+y=7$ and $x^x+y^y=7\times 41$
