Factorise each of the following expressions.
(i) 25x2y2 - 20xy2z + 4y2z2
(ii) 4x2 - 4
x + 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 - 4
x + 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)
= (5xy)2 - 2൵xy × 2yz + (2yz)2
= (5xy + 2yz)2
= y2 (5x + 2z)2
(ii) 4x2 - 4
x + 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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