Advanced Factoring
Difference of Squares
A difference of squares is a special factoring pattern: one perfect square minus another perfect square.
The difference of squares formula
The pattern is a² − b² = (a − b)(a + b). The middle terms cancel when the brackets are expanded, leaving only the two squares.
How to spot and factor it
- Check that there are two terms separated by subtraction.
- Confirm that both terms are perfect squares.
- Take the square root of each term.
- Write one minus bracket and one plus bracket.
Worked example
Factor x² − 16
- x² is the square of x.
- 16 is the square of 4.
- Use the same terms with opposite signs.
x² − 16 = (x − 4)(x + 4).
Common mistakes
- Using the rule for a sum of squares.
- Forgetting one plus and one minus sign.
- Missing a GCF that should be factored out first.
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