Q11 of 30 Page 2

Factorise each of the following expressions.
(i) 25x2y2 - 20xy2z + 4y2z2
(ii) 4x2 - 4x + 7
(iii) 
(iv) 4a2 + 12ab + 9b2 - 8a - 12b

(i) 25x2y2 - 20xy2z + 4y2z2
    = (5xy)2 - 2൵xy × 2yz + (2yz)2
    = (5xy + 2yz)2
    = y2 (5x + 2z)2
(ii) 4x2 - 4x + 7
     = (2x)2 + 2൲x ×+()2 = (2x +)2 
(iii) 
    = 
(iv) 4a2 + 12ab + 9b2 - 8a - 12b
     = (4a2 + 12ab + 9b2) - 4(2a + 3b)
     = (2a)2 + 2 × 2a × 3b + (3b)2 - 4(2a + 3b)
     = (2a + 3b)2 - 4(2a + 3b)
     = (2a + 3b) (2a + 3b - 4)

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9 Factorise
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(i) 6ab - b2 + 12ac - 2bc
(ii) x2 + y - xy - x
(iii) x3 - 2x2y + 3xy2 - 6y3
(iv) a(a + b - c) – bc 12 Factorise
(i) 25x2 - 36y2
(ii) 2ab - a2 - b2 + 1
(iii) 36a2 - 12a + 1 - 25b2
(iv) a4 - 81b4
(v) a12b4 - a4b12
(vi) 4x2 - 9y2 - 2x - 3y   13 Factorise by completing the squares.
(i) a4 + a2 + 1
(ii) y4 + 5y2 + 9
(iii) x4 + 4
(iv) x4 + 4x2 + 3