Verified answer

When we add any value to another value, then the value that we added equals the difference between the initial and final value. Let us understand it by an example,

Suppose there is a number X and we added Y to it to get Z, then

=> Y = Z - X

If you still don't understand it, then I will explain in a more clear way, Suppose we have 10 rupees, and someone gave us 5 rupees, now we have 15 rupees.

We had 10 rupees, and now we have 15, so the difference between these two is the same thing we added i.e., 5 rupees.

Now, let us get back to the question, Here we have the initial value as x² + xy + y² and the final value is given as 2x² + 3xy

As from the above examples, the difference between these two algebraic expressions is what we should add.

So,

=> Z = ( 2x² + 3xy ) - ( x² + xy + y² )

=> Z = 2x² + 3xy - x² - xy - y²

Writing like terms after each other,

=> Z = 2x² - x² + 3xy - xy - y²

=> Z = x² + 2xy - y²

=> Z = x² - y² + 2xy

Hence, your answer is x² - y² + 2xy

[tex]a + ( {x}^{2} + {y}^{2} + xy) = 2 {x}^{2} + 3xy[/tex]

[tex]a = {2x}^{2} + 3xy -( {x}^{2} + {y}^{2} + xy)[/tex]

[tex]a = {2x}^{2} + 3xy - {x}^{2} - {y}^{2} - xy[/tex]

[tex]a = 2 {x}^{2} - {x}^{2} + 3xy - xy - {y}^{2} [/tex]

[tex]a = {x}^{2} - {y}^{2} + 2xy[/tex]