If $x$ is a real number, find $49x^2+14x(19-7x)+(19-7x)^2$.
I notice that this expression has the form $a^2+2ab+b^2$, where $a=7x$ and $b=19-7x$. This is a perfect square, so I can rewrite it as $(a+b)^2$. In this case, that means $(7x+(19-7x))^2$. Simplifying the parentheses, I get $(19)^2$. This is just $361$, regardless of the value of $x$. 