Question

Factorise the following
(i)`9x^(2)-12x+3` (ii) `9x^(2)-12x+4`

Answer 1

(i) `9x^(2)-12+3=3(3x^(2)-4x+1)` [taking 3 common factor ]
`=3(3x^(2)-3x-x+1)` [by splitting middle term]
`=3[3x(x-1)-1(x-1)]=3(3x-1)(x-1)`
(ii) `9x^(2)-12x+4=(3x)^(2)-2xx3xxx2+(2)^(2)`
`=(3x-2)^(2)` [ using identity ,`(a-b)^(2)=a^(2)-2ab+b^(2)]`
`=(3x-2)(3x-2)`