Question

If A = 7x² + 5xy − 9y², B = −4x² + xy + 5y² and C = 4y² − 3x² − 6xy then show that A + B + C = 0.

Answer 1

A = 7x² + 5xy − 9y²
B = −4x² + xy + 5y²
C = 4y² − 3x² − 6xy

Substituting the values of A, B and C in A+B+C:
= (7x² + 5xy − 9y²)+(−4x² + xy + 5y²)+(4y² − 3x² − 6xy)
= 7x² + 5xy − 9y²−4x² + xy + 5y²+4y² − 3x² − 6xy

Rearranging and collecting the like terms:
(7-4-3)x² + (5+1-6)xy +(−9+5+4)y²
= (0)x² + (0)xy + (0)y²
= 0
$\Rightarrow \mathrm{A}+\mathrm{B}+\mathrm{C}=0$