Advanced MathEasy–MediumProduct of conjugates
Advanced Math practice question
Which expression is equivalent to (3x + 2)(3x − 2)?
- A. 9x² − 4Correct
- B. 9x² + 4
- C. 9x² − 12x − 4
- D. 3x² − 4
Answer: A. 9x² − 4
The two factors differ only in the middle sign, so the middle terms cancel: 9x² − 6x + 6x − 4 = 9x² − 4. This is the difference-of-squares pattern in reverse.
Why the other answers are wrong
- B. 9x² + 4
- The constant is 2 × (−2) = −4, not +4.
- C. 9x² − 12x − 4
- The middle terms −6x and +6x cancel each other; there's no −12x.
- D. 3x² − 4
- (3x)² is 9x², not 3x². The coefficient is squared too.
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For x ≠ 0, which expression is equivalent to (x² + 3x) / x? - Easy–Medium
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