Divisibility proofs with identities

Divisibility proofs with identities

Secondary 2
TGM Original Questions
  1. Prove that \((5n+2)^2-(3n-2)^2\) is always even for every integer \(n\).
  2. If \(x\) is a positive integer, show that \((6x+1)^2-4(6x+1)-3\) is always divisible by 6.

Solution:

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Answer:(a) Always even; (b) always divisible by \(6\).

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