Key idea. Add and subtract the same term to reveal a square.

1. Compare with \((x^2+1)^2=x^4+2x^2+1\). Our expression has only \(x^2\) in the middle, so write

   \[x^4+x^2+1=(x^2+1)^2-x^2.\]

2. This is a difference of squares:

   \[\bigl((x^2+1)-x\bigr)\bigl((x^2+1)+x\bigr).\]

3. Rearranging the terms in each bracket gives \((x^2-x+1)(x^2+x+1)\).

Remember. Adding and subtracting the same quantity changes the form without changing the value.