Rational numbers $a$ and $b$ satisfy the equality $$a^3b+ab^3+2a^2b^2+2a + 2b + 1 = 0. $$Prove that the number $1-ab$ is the square of the rational numbers.
Source: All-Russian MO 2009 Regional 9.2
Tags: algebra, Perfect Square
Rational numbers $a$ and $b$ satisfy the equality $$a^3b+ab^3+2a^2b^2+2a + 2b + 1 = 0. $$Prove that the number $1-ab$ is the square of the rational numbers.