a) Factor 9x² + y² + z² - 6xy + 2yz - 6xz
This looks a lot like
(x+y+z)² = x² + y² + z²+ 2xy + 2yz + 2xz
except instead of x there's (-3x). So this must be
(-3x+y+z)² = (-3x)² + y² + z² + 2((-3x)y + (-3x)z + yz)
= 9x² + y² + z² - 6xy + 2yz - 6xz
Looks good.
Answer: (-3x+y+z)²
Since it's a square we could also negate the inside and write this (3x-y-z)²
b) I'll guess that says we want to evaluate this when x=1, y=2, z= -1
(-3(1) + 2 -1)² = (-2)² = 4
Answer: 4
