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**How to do GCSE Algebraic Proof **

==> How To Do Algebraic Proof GCSE Maths Lesson Slides

==> How To Do Algebraic Proof GCSE Maths Lesson Answers

1 Prove that (n + 1)^2 – (n – 1)^2 + 1 is always odd for all positive integer values of n.

2 Prove that (3n + 1)^2 – (3n –1)^2 is a multiple of 4, for all positive integer values of n.

3 Prove algebraically that the sum of the squares of any two consecutive numbers always leaves a remainder of 1 when divided by 4.

4 Prove algebraically that the difference between the squares of any two consecutive odd numbers is always a multiple of 8.

5 Prove algebraically that the sum of the squares of any three consecutive even numbers is always a multiple of 4.