Trying to find the right answer to this..

We know that (x - y) 3 = x 3 - y 3 - 3xy(x - y) | Using Identity VII ⇒ x 3 - y 3 = (x - y) 3 + 3xy(x - y) x 3 - y 3 = (x - y){(x - y) 2 + 3xy} ⇒ x 3 - y 3 = (x - y)(x 2 - 2xy + y 2 + 3ry) | Using Identity IV ⇒ x 3 - y 3 = (x - y)(x 2 + xy + y 2 ).

Coordinate Geometry

Question

Wired Faculty App

Verify: x³ - y³ = (x - y)(x² + xy + y²).

Answer

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).