What is the value of $ x^2 + 4y^2 + z^2 - 4xy +4 yz - 2xz $ ?
Answer & explanation
Correct answer: option 3
$ x^2 + 4y^2 + z^2 - 4xy +4 yz - 2xz $
= x2 + (2y)2 + z2 - 2.(x).(2y) + 2.(z).(2y) - 2.(x).(z)
= (-x)2 + (2y)2 + z2 + 2.(-x).(2y) + 2.(z).(2y) + 2.(-x).(z)
Comparing with (a + b +c )2 = a2 + b2+ c2 + 2ab + 2bc + 2ca
= (-x)2 + (2y)2 + z2 + 2.(-x).(2y) + 2.(z).(2y) + 2.(-x).(z)
= (2y - x + z)2