Question:
Factorise the following
(i) 9x2 -12x+ 3
(ii) 9x2 -12xy + 4
Solution:
(i) $9 x^{2}-12 x+3=3\left(3 x^{2}-4 x+1\right)$ [taking 3 common factor]
$=3\left(3 x^{2}-3 x-x+1\right)$ [by splitting middle term]
$=3[3 x(x-1)-1(x-1)]=3(3 x-1)(x-1)$
(ii) $9 x^{2}-12 x+4=(3 x)^{2}-2 \times 3 x \times 2+(2)^{2}$
$=(3 x-2)^{2}$[using identity, $(a-b)^{2}=a^{2}-2 a b+b^{2}$ ]
$=(3 x-2)(3 x-2)$