Algebraic Proof: Show That an Expression is Even

Published on September 22, 2026

Algebra

Prove algebraically that the expression n^2 - 2 - (n - 2)^2 is always an even number by expanding the brackets and factoring out a 2.

Question

Answer

Expand the squared term :

Substitute this expansion back into the original expression and simplify:

Factor out a to show the expression is a multiple of :

Since the expression can be written in the form

(where

is an integer because

is an integer), the expression is always an even number.

Final Answer:

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