Question
Verify: x3 - y3 = (x - y)(x2 + xy + y2).
Solution
We know that
(x - y)3 = x3 - y3 - 3xy(x - y)
| Using Identity VII
⇒ x3 - y3 = (x - y)3 + 3xy(x - y)
x3 - y3 = (x - y){(x - y)2 + 3xy}
⇒ x3 - y3 = (x - y)(x2 - 2xy + y2 + 3ry)
| Using Identity IV
⇒ x3 - y3 = (x - y)(x2 + xy + y2).
