Find the value
Question:

Find the value

$9(2 a-b)^{2}-4(2 a-b)-13$

Solution:

Let $2 a-b=x$

$=9 x^{2}-4 x-13$

Splitting the middle term,

$=9 x^{2}-13 x+9 x-13$

$=x(9 x-13)+1(9 x-13)$

$=(9 x-13)(x+1)$

Substituting x = 2a – b

= [9(2a − b) − 13](2a − b + 1)

= (18a − 9b − 13)(2a − b + 1)

$\therefore 9(2 a-b)^{2}-4(2 a-b)-13=(18 a-9 b-13)(2 a-b+1)$

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