a 2 ± 2ab + b 2 type expressions

4.         type expressions

When we multiply a number say 3 with itself i-e 3×3 then we get 9 or

If we multiply (a+b) with itself i-e (a+b)(a+b) then we will get   or

Similarly if we multiply (a-b) with itself i-e (a-b)(a-b) then we will get    or

So, we can say that (a+b) is two time factor of

and (a-b) is two time factor of 

Hence to factorize such expressions we try to make them a whole square of some algebric expression and in this way we get it two time factor and factorization is complete.

Example: Factorize  

Solution: 

To factorize this expression we try to make whole square of it

i-e