Answer:
[tex]2(x+1)(x-1)[/tex]
Step-by-step explanation:
QUESTION :-
- Factorise [tex][(x + 1) + (x - 1)]^2 - (x - 1)^2 - (x + 1)^2[/tex]
ALGEBRIC IDENTITIES USED IN THIS QUESTION :-
- [tex](x + y)^2 = x^2 + y^2 + 2xy[/tex]
- [tex](x-y)^2 = x^2 + y^2 - 2xy[/tex]
- [tex]x^2 - y^2 = (x+y)(x-y)[/tex]
PROCEDURE :-
[tex][(x + 1) + (x - 1)]^2 - (x - 1)^2 - (x + 1)^2[/tex]
[tex]=> [ x + 1 + x - 1]^2 - [(x-1)^2 + (x+1)^2][/tex]
[tex]=> [2x]^2 - [(x^2 + 1 - 2x )+(x^2 + 1 + 2x)][/tex]
[tex]=> 4x^2 - [x^2 + x^2 + 2x - 2x + 1 + 1][/tex]
[tex]=> 4x^2 - [2x^2 + 2][/tex]
[tex]=> 4x^2 - 2x^2 - 2[/tex]
[tex]=> 2x^2 - 2[/tex]
[tex]=> 2(x^2 - 1)[/tex]
[tex]=> 2(x^2 - 1^2)[/tex]
[tex]=> 2(x+1)(x-1)[/tex]
