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

Study for the 8th Grade Mathematics Test. Prepare with multiple choice questions, each with hints and explanations. Get ready for your exam!

Multiple Choice

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

Explanation:
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.

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