Divisibility proofs with identities

Divisibility proofs with identities

Secondary 2

4 marks

TGM Original Questions

Prove that \((5n+2)^2-(3n-2)^2\) is always even for every integer \(n\).[4]

Solution:

Solution locked

680+ questions here come with free worked solutions. A free account saves your questions and progress; this one needs a course plan.

Create free account Sign in Get the E Math course · from S$29.98/mo E Math tuition

Create a free account to practise similar questions.

Create free account Sign in Get the E Math course · from S$29.98/mo E Math tuition

Answer:\(2[8n(n+2)]\). The bracket is an integer when \(n\) is an integer, so the expression is even.

Need help? Join our E-Maths tuition for O-Level success.