Factor x^2 - 9.

Factor x^2 - 9.

• A. (x-9)(x+1)
• B. (x-3)(x+9)
• C. (x-3)(x+3)
• D. (x+3)(x+9)

Answer: (C)

This is a difference of squares. When you have x^2 minus 9, you can see it as x^2 minus 3^2. The pattern a^2 minus b^2 factors as (a − b)(a + b). Here, a is x and b is 3, so the factors are (x − 3)(x + 3). If you multiply (x − 3)(x + 3), you get x^2 + 3x − 3x − 9, and the middle terms cancel, leaving x^2 − 9. That’s why this pairing works. The other options don’t give x^2 − 9 when expanded. They introduce different middle terms or constants, so they don’t match the original expression.

This is a difference of squares. When you have x^2 minus 9, you can see it as x^2 minus 3^2. The pattern a^2 minus b^2 factors as (a − b)(a + b). Here, a is x and b is 3, so the factors are (x − 3)(x + 3).

If you multiply (x − 3)(x + 3), you get x^2 + 3x − 3x − 9, and the middle terms cancel, leaving x^2 − 9. That’s why this pairing works.

The other options don’t give x^2 − 9 when expanded. They introduce different middle terms or constants, so they don’t match the original expression.