Question

one of the factor for 2x^2+y^2+8z^2-2√2xy-4√2yz+8xz​

Answer 1

Answer:

Given 2x2 + y2 + 8z2 – 2√2xy + 4√2yz – 8xz

Using identity,

(x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx

We can say that,

x2 + y2 + z2 + 2xy + 2yz + 2zx = (x + y + z)2

2x2 + y2 + 8z2 – 2√2xy + 4√2yz – 8xz

= (-√2x)2 + (y)2 + (2√2z)2 + (2 × -√2x × y) + (2 × y × 2√2z) + (2 × 2√2 × -√2x)

= (-√2x + y + 2√2z)2

= (-√2x + y + 2√2z)(- √2x + y + 2√2z)