factorize x^3-x — step-by-step solution

Let's factorize in

ℝ

x^{3} - x

This expression can be factorized into:

x \cdot (x^{2} - 1)

⇥Let's factor in

ℝ

(x^{2} - 1)

⇥For

x^{2} - 1

, we recognize a difference of two squares:

x^{2} - 1^{2}

. Apply

a^{2} - b^{2} = (a - b) \cdot (a + b)

, with

a = x

and

b = 1

▷The factor

(x^{2} - 1)

factors as:

(x + 1) \cdot (x - 1)

ⓘ Factor out the common factor

x

▶Factored expression:

x \cdot (x + 1) \cdot (x - 1)