[tex]a^8-a^2b^6=a^2(a^6-b^6)\qquad\text{use}\ (x^n)^m=x^{nm}\\\\=a^2[(a^3)^2-(b^3)^2]\qquad\text{use}\ (x-y)(x+y)=x^2-y^2\\\\=a^2(a^3-b^3)(a^3+b^3)\qquad\text{use}\ x^3\pm y^3=(x\pm y)(x^2\mp xy+y^2)\\\\=\boxed{a^2(a-b)(a+b)(a^2+ab+b^2)(a^2-ab+b^2)}[/tex]
