What should be subtracted from x2 – xy + y2 – x + y + 3 to obtai

1.	What should be subtracted from x2 – xy + y2 – x + y + 3 to obtain −x2 + 3y2 − 4xy + 1?
Answer» Let ‘E’ be the required expression. Then, we have x² – xy + y²– x + y + 3 – E = – x² + 3y² – 4xy + 1 Therefore, E = (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

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

Answer»

Let ‘E’ be the required expression. Then, we have

x² – xy + y²– x + y + 3 – E = – x² + 3y² – 4xy + 1

Therefore, E = (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