Question

Factorise [(x + 1) + (x - 1)]^2 - (x - 1)^2 - (x + 1)^2

Answer 1

`2(x+1)(x-1)`

Explanation:

QUESTION :-

• Factorise
  `[(x + 1) + (x - 1)]^2 - (x - 1)^2 - (x + 1)^2`

ALGEBRIC IDENTITIES USED IN THIS QUESTION :-

• 
  `(x + y)^2 = x^2 + y^2 + 2xy`

• 
  `(x-y)^2 = x^2 + y^2 - 2xy`

• 
  `x^2 - y^2 = (x+y)(x-y)`

PROCEDURE :-

`[(x + 1) + (x - 1)]^2 - (x - 1)^2 - (x + 1)^2`

`=> [ x + 1 + x - 1]^2 - [(x-1)^2 + (x+1)^2]`

`=> [2x]^2 - [(x^2 + 1 - 2x )+(x^2 + 1 + 2x)]`

`=> 4x^2 - [x^2 + x^2 + 2x - 2x + 1 + 1]`

`=> 4x^2 - [2x^2 + 2]`

`=> 4x^2 - 2x^2 - 2`

`=> 2x^2 - 2`

`=> 2(x^2 - 1)`

`=> 2(x^2 - 1^2)`

`=> 2(x+1)(x-1)`

Answer 2

2(x+1)(x-1)

Explanation: