Question

Factorise 9 X square + Y square + Z square - 6 X Y + 2 Y Z - 6 x z hence find its value when X is equals to 1 by equal to 2 and Z = 2 - 1

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Answer 1

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