(i) We have,
9x2 + 4y2 + 16z2 – 12xy – 16yz + 24xz
= (3x)2 + (- 2y)2 + (4z)2 + 2(3x)(- 2y) + 2(- 2y)(4z) + 2(3x)(4z)
[∵ a2 + b2 + c2 + 2ab + 2bc + 2ca = (a + b + c)2]
= (3x – 2y + 4z)2
= (3x – 2y + 4z)(3x – 2y + 4z)
(ii) We have,
x2 + 2y2 + 8z2 + 2√2xy – 8yz – 4√2xz
= (x)2 + (√2y)2 + (- 2√2z)2 + 2(x)(√2y) + 2(√2y)(- √2z) + 2(x)(- 2√2z)
[∵ a2 + b2 + c2 + 2ab + 2bc + 2ca = (a + b + c)2]
= (x + √2y – 2√2z)2
= (x + √2y – 2√2z)(x + √2y – 2√2z)