Structure Recognition Math Example 3

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Example 3

easy
Identify the structure and factorise: a2−b2a^2 - b^2.

Solution

  1. 1
    Recognise: a2−b2a^2 - b^2 is a difference of two squares.
  2. 2
    Apply the identity: a2−b2=(a−b)(a+b)a^2 - b^2 = (a-b)(a+b).

Answer

a2−b2=(a−b)(a+b)a^2-b^2 = (a-b)(a+b)
The difference of squares is one of the most important algebraic structures to recognise. It appears constantly in factoring, simplifying rational expressions, and integration.

About Structure Recognition

The skill of identifying that a given mathematical expression or problem belongs to a known family or matches a recognizable pattern.

Learn more about Structure Recognition →

More Structure Recognition Examples

Example 1 easy

Recognise and name the algebraic structure in [formula], then factorise.

Example 2 medium

Identify the structure in [formula] and use it to simplify [formula].

Example 4 medium

Recognise the structure in the sum [formula] and compute it using the geometric series formula.

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