Question

Question 27
Factorise the following:

$\left(i\right)9x^2–12x+3$

$\left(ii\right)9x^2–12x+4$

Answer 1

$\left(i\right)9x^2–12x+3=3(3x^2–4x+1)$ [taking 3 as common ]
$=3(3x^2–3x–x+1)$ [By spitting the middle term]
$=3\left[3x\right(x-1)–1(x–1\left)\right]=3\left[\right(3x-1\left)\right(x–1\left)\right]$

$\left(ii\right)9x^2–12x+4=(3x{)}^2–2\times 3x\times 2+(2{)}^2$
$=(3x-2{)}^2$ [Using the identity, $(a-b{)}^2=a^2–2ab+b^2$]
$=(3x–2)(3x–2)$