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

= 9c^{2} – 4c - 13

= 9c^{2} – 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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