we are given
[tex](x^3)^2-1[/tex]
Let's assume x^3 as a
[tex](x^3)^2-1=a^2-1[/tex]
now, we can factor
and we get
[tex]a^2-1=(a-1)(a+1)[/tex]
now, we can plug back 'a'
and we get
[tex](x^3)^2-1=(x^3-1)(x^3+1)[/tex]
now, we can factor again
we know that
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]
so, we get
[tex](x^3)^2-1=(x^3-1)(x+1)(x^2-x+1)[/tex]
now, we can use formula
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]
we can plug it
[tex](x^3)^2-1=(x-1)(x^2+x+1)(x+1)(x^2-x+1)[/tex]
we can rearrange it
[tex](x^3)^2-1=(x-1)(x+1)(x^2-x+1)(x^2+x+1)[/tex]..............Answer
