Factor x^2 - 9.

Factor x^2 - 9.

• A. (x+3)^2
• B. (x-3)(x+3)
• C. x^2-9
• D. (x-9)

Answer: (B)

This is a difference of squares. When you have a square minus another square, it factors into the product of the sum and the difference of the roots: a^2 − b^2 = (a − b)(a + b). Here a^2 is x^2 and b^2 is 9, so with a = x and b = 3 you get (x − 3)(x + 3). Expanding this confirms the factorization: (x − 3)(x + 3) = x^2 − 9. The other forms don’t fit because (x + 3)^2 would give x^2 + 6x + 9, which is not x^2 − 9; x^2 − 9 is just the original expression and isn’t a factorization; and (x − 9) is not a product of two binomials and does not multiply out to x^2 − 9.

This is a difference of squares. When you have a square minus another square, it factors into the product of the sum and the difference of the roots: a^2 − b^2 = (a − b)(a + b). Here a^2 is x^2 and b^2 is 9, so with a = x and b = 3 you get (x − 3)(x + 3). Expanding this confirms the factorization: (x − 3)(x + 3) = x^2 − 9.

The other forms don’t fit because (x + 3)^2 would give x^2 + 6x + 9, which is not x^2 − 9; x^2 − 9 is just the original expression and isn’t a factorization; and (x − 9) is not a product of two binomials and does not multiply out to x^2 − 9.