^{The sum :2xy+4yz+5xy+3yz-6xy}

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Solution

your questian can be re arranged as

(2xy+5xy-6xy)+(4yz+3yz)

(by grouping similar terms xy and yz)

=xy+7yz

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Simplify:

(2xy + 4yz + 9) - (3yz - 3xy - 1)

$4 x y - 5 y z - 7 z$

$- 5 x y + 2 y z + z x$

$- 2 x y - 3 y z + 3 z x$

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When $7 x y + 5 y z - 3 z x$ , $4 y z + 9 z x - 4 y$ and $- 3 x z + 5 x - 2 x y$ are added, we get $5 x y + 9 y z + 3 z x + 5 x - 4 y$ .

x^{2} + 2 x y + 3 y^{2}, 3 z^{2} + 2 y z + y^{2}, x^{2} + 3 z^{2} + 2 x z, z^{2} - 3 x y - 3 y z

2 x^{2} + 3 y^{2} + 4 z^{2} - \sqrt{6} x y - 2 \sqrt{3} y z - 2 \sqrt{2} x z = 0

(2 x^{2} + 3 y^{2} + 16 z^{2} + 2 \sqrt{6} x y - 8 \sqrt{3} y z - 8 \sqrt{2} x z)

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