The square root of `(xy + xz - yz)^(2) - 4xyz (x -y)` is _____

Options

A. `xy + yz - 2xyz`
B. `(x + y - 2xy)`
C. `(xy + 3 - y)`
D. `(xy + yz - zx)`

Answer

D

Explanation

`(xy +xz -yz)^(2) - 4xyz (x-y)`
`= (xy +z (x -y))^(2) -4 (xy) [z (x -y)]`
`= [xy -z (x -y)]^(2)`
`[ :' (a +b)^(2) -4ab = (a-b)^(2)]`
`=(xy - zx + yz)^(2)`
`= (xy + yz - zx)^(2)`
`:.` The square root of the given expression is `(xy + yz - zx)`