Factorise
(i) x2 + y2 + 9z2 + 2xy + 6yz + 6xz,
(ii) x2 + 4y2 + 9z2 – 4xy – 12yz + 6xz
(i) x2 + y2 + 9z2 + 2xy + 6yz + 6xz
= x2+(y)2+(3z)2+ 2(x)(y)+2(y)(3z)+2(x)(3z)
= (x + y + 3z)2
(ii) x2 + 4y2 + 9z2 _ 4xy – 12yz + 6xz
= x2 + (2y)2 + (3z)2 - 2(x)(2y) - 2(2y)(3z)+ 2(x)(3z)
= x2 + (2y)2 + (3z)2 + 2(x)(-2y) + 2(-2y)(3z) + 2(x)(3z)
= (x - 2y + 3z)2