Answer
$$\cos^4x+2\cos^2x+1=(\cos^2 x+1)^2$$
Work Step by Step
$$A=\cos^4x+2\cos^2x+1$$
To make the matter easier, we would take $u=\cos^2 x$, which means $u^2=(\cos^2 x)^2=\cos^4 x$.
Therefore, $$A=u^2+2u+1$$
So now we can see that this is a form of $(a+b)^2=a^2+2ab+b^2$ with $a=u$ and $b=1$. That shows,
$$A=(u+1)^2$$
Eventually, $$A=(\cos^2 x+1)^2$$
