Q. 194.1( 7 Votes )

Resolve each of t

Answer :

Here, coefficient of (2a – b)2 = 1, coefficient of (2a – b) = 2 and constant term = - 8

We shall now split up the coefficient of middle term i.e., 2 into two parts whose sum is 2 and product is -8 (1) = - 8


Clearly,


4 - 2 = 2 and,


4 (-2) = - 8


So, we replace 2 (2a – b) = 4 (2a –b) – 2 (2a – b)


Thus, we have


(2a – b)2 + 2 (2a – b) – 8 = (2a – b)2 + 4 (2a – b) – 2 (2a – b) - 8


= (2a – b) (2a – b + 4) – 2 (2a – b + 4)


= (2a – b – 2) (2a – b + 4)


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