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Factorise
(i) x
3
+ 9x
2
+ 27x + 27
(ii) x
3
– 9x
2
y + 27xy
2
– 27y
3
(i) x
3
+9x
2
+ 27x + 27
= (x)
3
+ 3(x)
2
(3)+3(x)(3)
2
+ (3)
3
= (2x + 3)
3
(ii) x
3
–9x
2
y + 27xy
2
– 27y
3
= x
3
–3(x)
2
(3y)+3(x)(3y)
2
– (3y)
3
= (x – 3y)
3
16
