Factorise:

Question:

Factorise:
9a2 − b2 + 4b − 4

Solution:

We have:

$9 a^{2}-b^{2}+4 b-4=9 a^{2}-\left(b^{2}-4 b+4\right)$

$=(3 a)^{2}-(b-2)^{2}$

$=\{3 a+(b-2)\}\{3 a-(b-2)\}$

$=(3 a+b-2)(3 a-b+2)$

$\therefore 9 a^{2}-b^{2}+4 b-4=(3 a+b-2)(3 a-b+2)$

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