# Algebraic Proof

# Understanding Algebraic Proof

- An
**algebraic proof**involves proving statements by using algebraic manipulations. - These proofs can test understanding of the properties of numbers, algebraic manipulation, and logical thought processes.

## Basic Elements of Proof

**Statements**: These are the mathematical expressions or equations that are the substance of the proof.**Assumptions or givens**: These are the facts or conditions that you are allowed to accept as true without proof.**Logical reasoning**: This is the method used to advance from the assumptions to the conclusion. It’s important to be clear and precise in your reasoning.

## Techniques

**Substitution**: This involves replacing variables with numbers or expressions in order to simplify a problem or prove a claim.**Simplification**: This involves reducing an expression to its most basic form - for instance, by using**BIDMAS**(brackets, indices, division/multiplication, addition/subtraction) order of operations or by collecting like terms.

## Example of Use

**Justifying solutions**: Whenever you solve an equation, you usually perform a series of steps that could qualify as a proof. By showing each step, you demonstrate that your solution is correct.

## Key Steps in Algebraic Proof

**Understand the proposition**: Deduce what needs to be proved.**Formulate a plan**: Think about the steps to take or strategies to use.**Carry out the proof**: Apply your plan, providing each step of your reasoning.**Review and refine**: Once a result is obtained, check your work and make sure your argument is clear and logical.

Remember, algebraic proofs require both algebraic skill and logical reasoning. They are a fundamental part of advanced mathematical study.