Question

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

Answer 1

Answer:

2(x+1)(x-1)

Step-by-step explanation:

Answer 2

Answer:

$2(x+1)(x-1)$

Step-by-step 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 :-

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

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

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

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

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

$=> 4x^2 - 2x^2 - 2$

$=> 2x^2 - 2$

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

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

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