Question

If P = 7x² + 5xy − 9y², Q = 4y² − 3x² − 6xy and R = −4x² + xy + 5y², show that P + Q + R = 0.

Answer 1

Given P = 7x² + 5xy − 9y², Q = 4y² − 3x² − 6xy and R = −4x² + xy + 5y²

Now we have to prove P + Q + R = 0,

Consider P + Q + R = (7x² + 5xy – 9y²) + (4y² – 3x² – 6xy) + (- 4x² + xy + 5y²)

= 7x² + 5xy – 9y² + 4y² – 3x² – 6xy – 4x² + xy + 5y²

Collecting positive and negative like terms together, we get

= 7x²– 3x² – 4x² + 5xy – 6xy + xy – 9y² + 4y² + 5y²

= 7x²– 7x² + 6xy – 6xy  – 9y² + 9y²

= 0