Answer
$(x^2-x-1)(x^2+x+1)$
Work Step by Step
The product of a binomial sum and a binomial difference is: $(A+B)(A-B)=A^2-B^2$.
The square of a binomial sum is: $(A+B)^2=A^2+2AB+B^2$.
The square of a binomial difference is: $(A-B)^2=A^2-2AB+B^2$.
Hence here: $x^4-(x^2+2x+1)=\\=(x^2)^2-((x)^2+2\cdot1\cdot x+1^2)=\\=(x^2)^2-(x+1)^2\\=(x^2-x-1)(x^2+x+1)$
