Simplify the expression: $2 x^{2} + 3 y^{2} - 5 x y + 5 x^{2} - y^{2} + 6 x y - 3 x^{2}$

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Solution

Given expression: $2 x^{2} + 3 y^{2} - 5 x y + 5 x^{2} - y^{2} + 6 x y - 3 x^{2}$
Simplifying the expression:
To simplify an expression, all the like terms are to be grouped and added.
So, the given expression can be written as:
$(2 x^{2} - 3 x^{2} + 5 x^{2}) + (3 y^{2} - y^{2}) + (6 x y - 5 x y)$
$= 4 x^{2} + 2 y^{2} + x y$
Therefore, the simplified expression is $4 x^{2} + 2 y^{2} + x y$

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