Question

$2x^2 + y^2 + 8z^2 - 2 \sqrt{2} xy + 4 \sqrt{2} yz - 8xz$
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Answer 1

${ \small{2x^2 + y^2 + 8z^2 - 2 \sqrt{2} xy + 4 \sqrt{2} yz - 8xz}} \\ { \mathtt{\boxed{ \small{ {( - \sqrt{2} x)}^{2} + {(y)}^{2} + {(2 \sqrt{2} z)}^{2} + 2[( - \sqrt{2}x )(y) + (y)(2 \sqrt{2}z ) + (2 \sqrt{2z} )( - \sqrt{2} x)]}}}} \\ \\ = > { \mathbf{{( - \sqrt{2}x + y + 2 \sqrt{2} z )}^{2} }}$