1)
=a^4+2a^2+1-a^2
=(a^2+1)^2-a^2
=(a^2-a+1)(a^2+a+1)
2)
=a^4+4b^4-4a^2b^2
=(a^2+2b^2)^2-4a^2b^2
=(a^2-2ab+2b^2)(a^2+2ab+2b^2)
3)
=(8x^2+1)^2-16x^2
=(8x^2-4x+1)(8x^2+4x+1).
4)
=x^5+x^4+x^3-x^3+1
=x^2(x^2+x+1)-(x-1)(x^2+x+1)
=(x^2-x+1)(x^2+x+1)
5).
=x^7-x+x^2+x+1
=x(x^6-1)+x^2+x+1
=x(x^3-1)(x^3+1)+x^2+x+1
=x(x-1)(x^2+x+1)(x^3+1)+x^2+x+1
=(x^2+x+1)[(x^2-x)(x^3+1)+1]
6)
=x^8-x^2+x^2+x+1
=x^2(x-1)(x^2+x+1)(x^3+1)+x^2+x+1
Xong nhóm x^2+x+1 vào.
7)
=x^4-(2x-1)^2
=(x^2-2x+1)(x^2+2x-1)
8)
=(a^8+b^8)^2-a^8b^8
=(a^8-a^4b^4+b^8)(a^8+a^4b^4+b^8).