4x²+9y²+z²+12xy-6yz-4xz

4 x^{2} + 9 y^{2} + z^{2} + 12 xy - 6 yz - 4 xz = {(- 2 x)}^{2} + {(- 3 y)}^{2} + z^{2} + 2 (- 2 x) (- 3 y) + 2 (- 3 y) (z) + 2 (z) (- 2 x) = {(- 2 x - 3 y + z)}^{2} ANS . . . (Since {(a + b + c)}^{2} = a^{2} + b^{2} + c^{2} + 2 ab + 2 bc + 2 ca) Taking minus common = {(2 x + 3 y - z)}^{2} ANS . . .

4x2+9y2+z2+12xy-6yz-4xz