Add x2 + 2xy + y2 to the sum of x2 – 3y2and 2x2 – y2 + 9.

1.	Add x2 + 2xy + y2 to the sum of x2 – 3y2and 2x2 – y2 + 9.
Answer» Given x²+ 2xy + y², x² – 3y²and 2x²– y² + 9. First we have to find the sum of x² – 3y² and 2x² – y² + 9 = (x² – 3y²) + (2x² – y² + 9) = x² + 2x² – 3y² – y²+ 9 = 3x² – 4y² + 9 Now, required expression = (x² + 2xy + y²) + (3x² – 4y² + 9) = x² + 3x² + 2xy + y² – 4y² + 9 = 4x² + 2xy – 3y²+ 9

Answer»

Given x²+ 2xy + y², x² – 3y²and 2x²– y² + 9.

First we have to find the sum of x² – 3y² and 2x² – y² + 9

= (x² – 3y²) + (2x² – y² + 9)

= x² + 2x² – 3y² – y²+ 9

= 3x² – 4y² + 9

Now, required expression = (x² + 2xy + y²) + (3x² – 4y² + 9)

= x² + 3x² + 2xy + y² – 4y² + 9

= 4x² + 2xy – 3y²+ 9

Discussion