If X equal to 2 minus y then show that x cube + 6 X y + y cube minus 8

1.	If X equal to 2 minus y then show that x cube + 6 X y + y cube minus 8 equal to zero
Answer» Explanation: ∵ x = 2 - y ∴ x³ + 6XY + y³ - 8 = (2 - y)³ +6(2 - y)y + y³ - 8 Expanding (2 - y)³ using identity (x - y)³ = x³ - y³ +3xy² - 3x²y = 2³ - y³ + 3.2.y² - 3.2².y + 12Y - 6y² + y³ - 8 = 8 - y³ + 6y² - 12y + 12y - 6y² + y³ - 8 = 0 ... Hence Proved

If X equal to 2 minus y then show that x cube + 6 X y + y cube minus 8 equal to zero

Answer»

Explanation:

∵ x = 2 - y

∴ x³ + 6XY + y³ - 8

= (2 - y)³ +6(2 - y)y + y³ - 8

Expanding (2 - y)³ using identity (x - y)³ = x³ - y³ +3xy² - 3x²y

= 2³ - y³ + 3.2.y² - 3.2².y + 12Y - 6y² + y³ - 8

= 8 - y³ + 6y² - 12y + 12y - 6y² + y³ - 8

= 0 ... Hence Proved