Expand the product (x - 3)(x + 3) and express in standard form.

Expand the product (x - 3)(x + 3) and express in standard form.

• A. x^2 - 9
• B. x^2 + 9
• C. x^2 - 6x + 9
• D. x^2 + 6x + 9

Answer: (A)

When you multiply conjugates, the middle terms cancel and you end up with a difference of squares. Here, treat x as a and 3 as b in the pattern (a−b)(a+b) = a^2 − b^2. So (x−3)(x+3) becomes x^2 − 9. You can see this by FOIL: x·x = x^2, x·(+3) = 3x, (−3)·x = −3x, and (−3)·(+3) = −9. The +3x and −3x cancel, leaving x^2 − 9. In standard form, the terms are written in descending powers of x, so the result is x^2 − 9.

When you multiply conjugates, the middle terms cancel and you end up with a difference of squares. Here, treat x as a and 3 as b in the pattern (a−b)(a+b) = a^2 − b^2. So (x−3)(x+3) becomes x^2 − 9.

You can see this by FOIL: x·x = x^2, x·(+3) = 3x, (−3)·x = −3x, and (−3)·(+3) = −9. The +3x and −3x cancel, leaving x^2 − 9. In standard form, the terms are written in descending powers of x, so the result is x^2 − 9.