Question 27
Factorise the following:

$(i) 9 x^{2} - 12 x + 3$

$(i i) 9 x^{2} - 12 x + 4$

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Solution

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

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

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(i) 9 x^{2} - 12 x + 3

(i i) 9 x^{2} - 12 x + 4

Question 27
Factorise the following:

$(i) 9 x^{2} - 12 x + 3$

$(i i) 9 x^{2} - 12 x + 4$

9 x^{2} - 12 x + 4 - 4 y^{2}

2 x^{3} - 9 x^{2} + 12 x + 4

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