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a − b) x + (a + b) y = a 2 − 2ab − b 2 … (1)
(a + b) (x + y) = a 2 + b 2
(a + b) x + (a + b) y = a 2 + b 2 … (2)
Subtracting equation (2) from (1), we obtain
(a − b) x − (a + b) x = (a 2 − 2ab − b 2) − (a 2 + b 2)
(a − b − a − b) x = − 2ab − 2b 2
− 2bx = − 2b (a + b)
x = a + b
Using equation (1), we obtain
(a − b) (a + b) + (a + b) y = a 2 − 2ab − b 2
a 2 − b 2 + (a + b) y = a 2− 2ab − b 2
(a + b) y = − 2ab
(a + b) (x + y) = a 2 + b 2
(a + b) x + (a + b) y = a 2 + b 2 … (2)
Subtracting equation (2) from (1), we obtain
(a − b) x − (a + b) x = (a 2 − 2ab − b 2) − (a 2 + b 2)
(a − b − a − b) x = − 2ab − 2b 2
− 2bx = − 2b (a + b)
x = a + b
Using equation (1), we obtain
(a − b) (a + b) + (a + b) y = a 2 − 2ab − b 2
a 2 − b 2 + (a + b) y = a 2− 2ab − b 2
(a + b) y = − 2ab
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