Question

Question Number 14 please help me with this one

Answer 1

If a − b is divisible by 3, then a − b = 3k, for some integer k 

(a − b)² = (3k)² 

a² − 2ab + b² = 9k² 

a³ − b³ = (a−b) (a² + ab + b²) 

 = (a−b) (a² − 2ab + b² + 3ab) 

 = 3k (9k + 3ab) 

 = 3k * 3 (3k + ab) 

 = 9 k(3k+ab) 

Since k(3k+ab) is an integer, then 9k(3k+ab) is divisible by 9 

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