Algebraic proof · Grade 10
In Grade 10 you learn: showing that expressions are equal.
An algebraic proof shows that a statement is true for every number, not just for the examples you have tried. Write general numbers with letters — 2n for an even number, 2n + 1 for an odd one — then use algebra to show the result always has the form you need.
Key facts
- A multiple of k can be written as k × (an integer).
- Checking examples is not a proof — but one counterexample is enough to show a statement is false.
- An identity (≡) is true for every value; prove it by expanding one side until it matches the other.