Question

(3n - 1)² - 4 chia hết cho 3 với mọi n

Answer 1

(3n - 1)² - 4

= (3n - 1)² - 2²

= (3n - 1 - 2)(3n - 1 + 2)

= (3n - 3)(3n + 1)

= 3(n - 1)(3n + 1) \(⋮\) 3

Answer 2

Ta có:

\(\left(3n-1\right)^2-4\)

\(=\left(3n-1\right)^2-2^2\)

\(=\left(3n-1-2\right)\left(3n-1+2\right)\)

\(=\left(3n-3\right)\left(3n+1\right)\)

\(=3\left(n-1\right)\left(3n+1\right)\) chia hết cho 3 với mọi n