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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Updated on: 10-Oct-2022

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