# Difference of two squares

A special pattern: a squared number minus another squared number factorises into (a - b)(a + b).

Maths (school) · Part 02: Algebra basics · Card 7 of 8 · Last updated 2026-10-19

## Analogy

Like cutting a square from a bigger square and rearranging the L-shape into a rectangle.

## Example

**x^2 - 49**

49 is 7^2
x^2 - 7^2
= (x - 7)(x + 7)

## In practice

It gives a mental shortcut: 51 x 49 = (50 + 1)(50 - 1) = 2,500 - 1 = 2,499.

## Practice

### Flashcards

- **Factorise x^2 - 49.** (x - 7)(x + 7).

## Questions people ask

### Why is there no middle term?

When you expand (x - 7)(x + 7), you get -7x and +7x. They cancel each other out. That leaves only x^2 - 49. So an expression with just a square minus a square, and nothing in the middle, is a difference of two squares.

### Does it work for x^2 + 49?

No. A plus sign between two squares does not factorise using real numbers. The pattern needs a minus. So x^2 - 49 factorises, but x^2 + 49 stays as it is. Check the sign before you try. Brackets cannot make it, as no pair multiplies out to that.

## Related concepts

- [Factorising quadratics](https://studyvisually.com/learn/science/maths-school/maths-school-part-2/maths-school-part-2-concept-6)
- [Simplifying expressions](https://studyvisually.com/learn/science/maths-school/maths-school-part-2/maths-school-part-2-concept-1)
- [Substitution](https://studyvisually.com/learn/science/maths-school/maths-school-part-2/maths-school-part-2-concept-2)
- [Expanding brackets](https://studyvisually.com/learn/science/maths-school/maths-school-part-2/maths-school-part-2-concept-3)

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