Question

What should be subtracted from x² − xy + y² −x + y + 3 to obtain −x² + 3y² − 4xy + 1?

Answer 1

Let 'M' be the required expression. Then, we have
x² - xy + y² - x + y + 3 - M = - x² + 3y² - 4xy + 1
Therefore,
M = (x² - xy + y² - x + y + 3) - (- x² + 3y² - 4xy + 1)
= x² - xy + y² - x + y + 3 + x² - 3y² + 4xy - 1
Collecting positive and negative like terms together, we get
x² + x²- xy + 4xy + y²- 3y² - x + y + 3 - 1
= 2x² + 3xy- 2y²- x + y + 2