# GCSE Proofs

In these lessons, we will learn various mathematical proofs, suitable for GCSE Maths students.

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More GCSE Maths

#### Algebraic Proof

How to attempt typical GCSE Algebraic Proof questions?
Examples:

1. Prove (x + 10)2 - (x + 2)2 is divisible by 16, where x is a positive integer.
2. Prove the sum of three consecutive even integers is divisible by 6.
3. Prove that the product of two odd numbers is always odd.
4. Prove that when two consecutive integers are squared, that the difference is equal to the sum of the two consecutive integers.

#### Algebraic Proof

GCSE Maths revision tutorial video.
Examples:

1. Prove algebraically that the sum of two consecutive odd numbers is always a multiple of 4.
2. Prove algebraically that the product of two even numbers is always a multiple of 4.

#### Proof using Algebra

Examples:

1. Prove that (5n + 1)2 - (5n - 1)2 is a multiple of 5, for all positive integer values of n.
2. Prove that (n + 2)2 - (n - 12)2 is even, for all positive integer values of n.
3. Prove that the sum of any two consecutive odd numbers is always even.
4. Prove that the sum of the squares of any two consecutive numbers is always an odd number.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 