Algebraic Proof Written as Expressions

Algebraic Proof statements can be written as expressions usually using the letter "n". In the graphic below there are 6 statements that can written as an expression of n.

Algebraic Proof Example Question

The algebraic proof example below asks students to prove that the difference between 8¹² and 12⁷ is a multiple of 4. To answer this question first show that 8¹² is the same as 8¹ x 8¹¹ which is the same as (4 x 2 x 8¹¹). Next show that 12⁷ is the same as 12¹ x 12⁶ which is the same as (4 x 3 x 12⁶). As an extension to this problem students could show that the diference between 8^a and 12^b necessarily equals 4n.

'Prove that!'

Consider the conjecture below. Use proof by mathematical induction to come up with a solution.

Algebraic Proof Key Words

Terminology is important when applying algebraic proof. You'll want to have a good grasp of all the key words.

When proving a statement algebraically you will use expressions usually in the form of the letters n or x. For example, to prove that a number is even we show that n is divisible by 2, or that n is a multiple of 2.

The graphic above asks students to explain the difference between a 'conjecture' and a 'proof'. A conjecture presents an idea which is yet to be proven.  To learn more about the Poincare Conjecture see the article Grigori Perelman - The Mathematician Who Proved the Poincare Conjecture.