What is the value of $19^2 + 2(19) + 1$?
I notice that the expression is of the form $a^2 + 2a + 1$, which is a perfect square: $(a + 1)^2$. So I can rewrite the expression as $(19 + 1)^2$. That makes it easier to evaluate, since I just need to add 19 and 1 and then square the result. I get $(19 + 1)^2 = 20^2 = 400$. 