Difference of two squares

Definition

The identity $A^2-B^2=(A+B)(A-B)$ , used when one complete square is subtracted from another.

Specification A4 · Paper 1, Paper 2, Paper 3

Specification A4 · Paper 1, Paper 2, Paper 3

1
Always look for a common factor before using the difference of two squares or factorising a quadratic.
2
Do not apply the difference of two squares to a sum: $A^2+B^2$ does not factorise as .

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(

A

+

B)(A−

B)

Used by AQA and Edexcel

2

−

B2

(A+B)(A-B)

B2

(A+B)(A-B)

3

For a difference of two squares, check that there are exactly two square terms separated by subtraction: $A^2-B^2=(A+B)(A-B)$ .