Answer:
The factored form of x^3 -1 will be:
[tex]x^3-1^3=\left(x-1\right)\left(x^2+x+1\right)[/tex]
Step-by-step explanation:
Given the expression
[tex]x^3-1[/tex]
Rewrite 1 as 1³
[tex]=x^3-1^3[/tex]
[tex]\mathrm{Apply\:Difference\:of\:Cubes\:Formula:\:}x^3-y^3=\left(x-y\right)\left(x^2+xy+y^2\right)[/tex]
[tex]x^3-1^3=\left(x-1\right)\left(x^2+x+1\right)[/tex]
[tex]=\left(x-1\right)\left(x^2+x+1\right)[/tex]
Thus, the factored form of x^3 -1 will be:
[tex]x^3-1^3=\left(x-1\right)\left(x^2+x+1\right)[/tex]
