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

2 Answers

4 votes

Answer:


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)

User Liastre
by
6.8k points
3 votes

Answer:

2(x+1)(x-1)

Explanation:

User JasonRDalton
by
6.8k points