(i) 4x2 + 9y2 + 25z2 + 12 xy + 30 yz + 20 xz
= (2x)2 + (3y)2 + (5z)2 + 2(2x)(3y) + 2(3y) + (5z) + 2 x 3y x 5z
= (2x + 3y + 5z)2
∵ (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
(ii) 25x2 + 4y2 + 9z2 – 20xy + 12yz – 30xz
= (5x)2 + (-2y)2 + (-3z)2 + 2(5x)(-2y) + 2(-2y)(-3z) + 2(-3z)(5x)
= (5x – 2y – 3z)2