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Factorise
(i) x
2
+ y
2
+ 9z
2
+ 2xy + 6yz + 6xz,
(ii) x
2
+ 4y
2
+ 9z
2
– 4xy – 12yz + 6xz
(i) x
2
+ y
2
+ 9z
2
+ 2xy + 6yz + 6xz
= x
2
+(y)
2
+(3z)
2
+ 2(x)(y)+2(y)(3z)+2(x)(3z)
= (x + y + 3z)
2
(ii) x
2
+ 4y
2
+ 9z
2
_
4xy – 12yz + 6xz
= x
2
+ (2y)
2
+ (3z)
2
- 2(x)(2y) - 2(2y)(3z)+ 2(x)(3z)
= x
2
+ (2y)
2
+ (3z)
2
+ 2(x)(-2y) + 2(-2y)(3z) + 2(x)(3z)
= (x - 2y + 3z)
2
29
