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Question

Factorise the expression: x2+1x2+22x2x
  1. (x+1x)(x1x2)
  2. (x1x)(x1x2)
  3. (x1x)(x+1x2)
  4. (x+1x)(x+1x2)


Solution

The correct option is D (x+1x)(x+1x2)
Given: x2+1x2+22x2x

Combining the first three terms and last two terms we get, =(x2+1x2+2)(2x+2x)

Applying the identity (a+b)2=a2+2ab+b2 we get,(x2+1x2+2)=(x+1x)2.

So, (x2+1x2+2)(2x+2x)=(x+1x)22(x+1x)

Taking (x+1x) common, we get,

(x+1x)(x+1x2)

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