Question

What is the factored form of x^3 -1

Answer 1

Answer:

The factored form of x^3 -1 will be:

$x^3-1^3=\left(x-1\right)\left(x^2+x+1\right)$

Step-by-step explanation:

Given the expression

$x^3-1$

Rewrite 1 as 1³

$=x^3-1^3$

$\mathrm{Apply\:Difference\:of\:Cubes\:Formula:\:}x^3-y^3=\left(x-y\right)\left(x^2+xy+y^2\right)$

$x^3-1^3=\left(x-1\right)\left(x^2+x+1\right)$

            $=\left(x-1\right)\left(x^2+x+1\right)$

Thus, the factored form of x^3 -1 will be:

$x^3-1^3=\left(x-1\right)\left(x^2+x+1\right)$