Basically presented with this, simplify
\begin{aligned} {\Bigl(\sqrt{x^2 + 2x + 1}\Big) + \Bigl(\sqrt{x^2 - 2x + 1}\Big)} \end{aligned}
Possible factorisations into both
\begin{aligned} {\Bigl({x + 1}\Big)^2}, {\Bigl({x - 1}\Big)^2} \end{aligned}
\begin{aligned} {\Bigl({1 + x}\Big)^2} , {\Bigl({1 - x}\Big)^2} \end{aligned}
Hence when simplified, answer has two possibilities. One independent of x, and the other not.
( Simplified Answers: 2x, 2 )
Why is one independent and the other not? If such is equal to 2, why then when, say x=2, the answer does not simplify to 2?