Factorise the following


Factorise the following

(i) 9x2 -12x+ 3          

(ii) 9x2 -12xy + 4


(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, $(a-b)^{2}=a^{2}-2 a b+b^{2}$ ]

$=(3 x-2)(3 x-2)$


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