Subtract the sum of $x^{2} + 2 x + 2$ and $x^{2} y + 3$ from the sum of $2 x^{2} + 5 x - 1$ and $y^{2} + x^{2} y - 3$ .

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Solution

Subtracting the expression
First find the sum of $x^{2} + 2 x + 2$ and $x^{2} y + 3$
$= x^{2} + 2 x + 2 + x^{2} y + 3$
Also, sum of $2 x^{2} + 5 x - 1$ and $y^{2} + x^{2} y - 3$
$= 2 x^{2} + 5 x - 1 + y^{2} + x^{2} y - 3$
According to the question.
$(2 x^{2} + 5 x - 1 + y^{2} + x^{2} y - 3) - (x^{2} + 2 x + 2 + x^{2} y + 3)$
Simplifying the expression.
$= (2 x^{2} + 5 x - 1 + y^{2} + x^{2} y - 3) - (x^{2} + 2 x + 2 + x^{2} y + 3)$
Rearrange like terms and then solving,
$= 2 x^{2} + 5 x - 1 + y^{2} + x^{2} y - 3 - x^{2} - 2 x - 2 - x^{2} y - 3 = 2 x^{2} - x^{2} + 5 x - 2 x + y^{2} + x^{2} y - x^{2} y - 1 - 3 - 2 - 3 = x^{2} + 3 x + y^{2} - 9$
Hence, the result is $x^{2} + y^{2} + 3 x - 9$ .

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