# Proof

- Created by: Josh
- Created on: 17-04-11 17:43

**Proof**

*To understand how to prove something algebraically, we must first ask ourselves: "What is a proof?"*

*A proof is simply a logical, step-by-step guide to demonstrate that a given rule or statement is ALWAYS correct. You cannot, therefore, prove something simply by giving an example, as this does not make something ALWAYS correct; although you may have demonstrated that your example fits the rule, you have not shown that the rule is correct in every instance.*

The best way to mathematically prove something is using algebra. Sometimes, a question may already give you the algebraic notation, for example:

"Prove that (2a - 1)^2 - (2b - 1)^2 = 4(a - b)(a + b - 1)"

Here, you would simply rearrange the left side to make it look like the right side of the equation, writing down each stage in your working, like so:

*(2a - 1)^2 - (2b - 1)^2*

*Expanding the brackets gives:*

*4a^2 - 2a - 2a + 1 - 4b^2 + 2b + 2b - 1*

*Collecting like terms gives:*

*4a^2 - 4a - 4b^2 + 4b*

*Taking out a factor of 4 gives:*

*4(a^2 - b^2 - a + b)*

*a^2 -*…

## Comments

No comments have yet been made