Difference of two squares

a² − b² = (a − b)(a + b). CAPS Grade 9 definition, worked example and related algebra practice.

a² − b² = (a − b)(a + b).

Definition

A difference of two squares is an expression with two perfect squares separated by a minus sign. It always factorises as a² − b² = (a − b)(a + b). It's one of the most used factorising patterns from Grade 9 to Grade 12.

Worked example

x² − 49 = (x − 7)(x + 7).

3x² − 12 = 3(x² − 4) = 3(x − 2)(x + 2): take out the common factor first.

4a² − 9b² = (2a − 3b)(2a + 3b).

Where it appears in the exam

Difference of two squares is part of the algebra section of CAPS Grade 9 Mathematics and appears in school tests and the end-of-year exam.

Step-by-step method

  1. Take out any common factor first.
  2. Check that both terms are perfect squares with a minus between them.
  3. Write the square root of each term: a and b.
  4. Factorise as (a − b)(a + b).

Common mistake

Trying to factorise a sum of two squares such as x² + 9, which does not factorise.

Related algebra terms

Frequently asked questions

What does difference of two squares mean in Grade 9 Maths?

A difference of two squares is an expression with two perfect squares separated by a minus sign. It always factorises as a² − b² = (a − b)(a + b). It's one of the most used factorising patterns from Grade 9 to Grade 12.

When do you learn about difference of two squares?

Difference of two squares is taught in the algebra section of CAPS Grade 9 Mathematics and is used again in Grades 10 to 12.

How do I practise questions involving difference of two squares?

Snap a question that uses difference of two squares into Snap&Learn with your grade set to Grade 9, or work through the Grade 9 topic guide and practice papers.

Snap&Learn gives South African Matric learners instant, CAPS-aligned, step-by-step Mathematics solutions. Snap or upload a question and the AI shows every method mark the way the NSC memo awards them. Your first three AI solutions are free.