To factor the expression x² – 9, we recognize it as a difference of two squares. The general form for factoring the difference of two squares is:
a² – b² = (a – b)(a + b)
In our case, we can identify:
- a² = x² ⟹ a = x
- b² = 9 ⟹ b = 3
Applying the difference of squares formula, we substitute a and b:
x² – 9 = (x – 3)(x + 3)
So, the factored form of the expression x² – 9 is (x – 3)(x + 3). This shows that the original quadratic can be expressed as a product of two binomials. Factoring like this is particularly useful because it can help us find the roots of the equation when set to zero, making it an essential technique in algebra.