Algebraic proof (AQA GCSE Further Maths): Flashcards

A logical argument using algebra to demonstrate mathematical statements are true

Begin with what you know (given info), work step-by-step

Writing the conclusion first instead of starting with known facts

Show it can be written as $n^2$ where $n$ is an integer

Expand, simplify, and factorise to identify perfect square

When proving expressions are always positive

$(x - a)^2 + b$, where if $b > 0$, expression is positive

Squared expressions are always $\geq 0$ (never negative)

Take half the coefficient of $x$ and square it

Factor and cancel common terms, then use properties

With the given expression, not the result to prove

Show every algebraic step clearly - don't skip steps

Clear statement matching what the question asked to prove

Writing conclusion first and working backwards

Forgetting to state variables are integers when crucial