Question

What should be added to x2 +xy+y2 to obtain 3x2 - 4xy - y2​

Answer 1

2x² - 5xy - 2y²

Explanation:

Subtract x² + xy + y² from 3x² - 4xy - y² to obtain the expression to be added

3x² - 4xy - y² - (x² + xy + y² ) ← distribute by - 1

=3x² - 4xy - y² - x² - xy - y² ← collect like terms

= 2x² - 5xy - 2y²

Thus

adding 2x² - 5xy - 2y² to x² + xy + y² gives 3x² - 4xy - y²