Question

write factors of a^3 - b^3

Answer 1

Hi,

Here is your answer

a³ - b³ = (a - b)³ + 3ab (a - b)
           = (a - b)³ + 3a²b - 3ab²
           = (a - b)³ + 3ab (a - b)
           = (a - b) [(a - b)² + 3ab)
           = (a - b) (a² + b² - 2ab + 3ab)
           = (a - b) (a² + b² + ab)
Therefore the factors of a³ - b³ are (a - b) (a² + b² + ab).

Hope this helps you.