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What should be added to $x^{2}\ +\ xy\ +\ y^{2}$ to obtain $2x^{2}\ +\ 3xy$?
Given :
The given terms are $x^{2} + xy + y^{2}$ and $2x^{2} + 3xy$
To do :
We have to find what term should be added to $x^{2}\ +\ xy\ +\ y^{2}$ to obtain $2x^{2}\ +\ 3xy$
Solution :
Let the term to be added be 'A'.
So, $A + x^{2} + xy + y^{2} =2x^{2} + 3xy $
$A = 2x^{2} + 3xy - ( x^{2} + xy + y^{2})$
Multiply $-$ inside the brackets,
$A = 2x^{2} + 3xy - x^{2} - xy - y^{2}$
$A = 2x^{2} - x^2 + 3xy - xy - y^2 $
$A = x^2 + 2xy - y^2$
Therefore, $x^2 + 2xy - y^2$ should be added to $x^{2}\ +\ xy\ +\ y^{2}$ to obtain $2x^{2}\ +\ 3xy$.
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