Tim Gan Math
Sign up free

Differences of squares of consecutive odd numbers

Differences of squares of consecutive odd numbers

IP 2
7 marks

Let \(n\) be a positive integer.

  1. Expand and simplify \((2n+1)^2-(2n-1)^2\). Hence show that the difference between the squares of two consecutive odd numbers is always a multiple of \(8\).[3]
  2. Without using a calculator, use (a) to evaluate \(1001^2-999^2\).[2]
  3. Explain why the difference between the squares of any two consecutive integers is always odd.[2]

Solution:

Solution locked

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

Create free accountSign inIP Math tuition

Create a free account to practise similar questions.

Create free accountSign inIP Math tuition
Answer:(a) \(8n\); a multiple of \(8\) (b) \(4000\) (c) \((n+1)^2-n^2=2n+1\), which is odd

Need help? Join our IP Math tuition programme.

Learn more