MAHARASHTRA Class 8: Factorisation Using Cubic Identities Videos | Algebraic Identities: Cubic Type

8³ = 512 and 9³ = 729

512 < 530 < 729

∴

∴

∴ 

(x − y)³ = x³ - 3x²y + 3xy² − y³

xy¹⁰z + xyz¹⁰

= xyz (y⁹ + z⁹)

= xyz [(y³)³ + (z³)³]

Here, a = y³ and b = z³

= xyz (y³+ z³) [(y³)² − y³z³ + (z³)²] ... using a³ + b³ = (a + b)(a² − ab + b²)

 = xyz (y³+ z³) (y⁶ − y³z³ + z⁶)

 =xyz (x + z) (x² − xz + z²) (y⁶ − y³z³ + z⁶) … using a³ + b³ = (a + b)(a² − ab + b²)