Q. 465.0( 2 Votes )

Factorize:

9(2a – b)2 – 4(2a – b) – 13

Answer :

We have,



Let 2a – b = c


Then,


9 (2a - b)2 – 4 (2a - b) - 13


Now by using middle-term splitting, we get


= 9c2 – 4c - 13


= 9c2 – 13c + 9c – 13


= c (9c – 13) + 1 (9c – 13)


= (c + 1) (9c - 13)


Now,


Replacing c by (2a - b) - 13, we get


9 (2a – b)2 – 4 (2a – b) - 13


= (2a – b + 1) [9 (2a – b) – 13]


= (2a – b + 1) (18a – 9b – 13)


Hence,


The given expression can be factorized as:



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