AlgebraEasy
Factor x² − 9
Recognize and factor a difference of two perfect squares.
Method: Difference of squares
Step-by-step solution
- 1
Identify both squares
x² is the square of x and 9 is the square of 3.
- 2
Apply the identity
Use a²−b²=(a−b)(a+b).
- 3
Check by expansion
The middle terms cancel and the product returns x²−9.
Final answer
Conjugate factors produce a difference of squares because their opposite middle terms cancel.
Common mistake
A sum of squares does not factor with the same real-number identity.
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