Question

20. Which of the following is the factorization of x3 – x?
(i) x(x – x2)
(ii) x[(1+ x) (1 – x)]
(iii) x(x2 – x)
(iv) x[(x + 1) (x – 1)]

Answer 1

Answer:

(iv)

Step-by-step explanation:

${x}^{3} - x \\ x( { x}^{2} - 1) \\ x(x - 1)(x + 1)$

(iv)

$x(x - 1)(x + 1)$

Answer 2

Answer:

x(x−1)(x+1)

Step-by-step explanation:

Given : x^3 - xx

3

−x

To Find : Factorize

Solution :

x^3 - xx

3

−x

Take x as common

x(x^2 - 1)x(x

2

−1)

Property : x^2-a^2=(x-a)(x+a)x

2

−a

2

=(x−a)(x+a)

Applying the property

x(x-1)(x+1)x(x−1)(x+1)

So, Factorization of x^3 - xx

3

−x is x(x-1)(x+1)x(x−1)(x+1)