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Addition and Subtraction of Algebraic Expression

Find the sum ...

Question

Find the sum of $x^{2} + 2 x y + 3 y^{2}, 3 z^{2} + 2 y z + y^{2}, x^{2} + 3 z^{2} + 2 x z, z^{2} - 3 x y - 3 y z$

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Solution

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

Grouping the like terms,
$= (x^{2} + x^{2}) + (2 x y - 3 x y) + (3 y^{2} + y^{2}) + (3 z^{2} + 3 z^{2} + z^{2}) + (2 y z - 3 y z) + (+ 2 x z)$

$= 2 x^{2} - x y + 4 y^{2} + 7 z^{2} - y z + 2 x z$

$= 2 x^{2} + 4 y^{2} + 7 z^{2} - x y - y z + 2 x z$

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