Advanced MathMediumProduct of conjugates in x²
Advanced Math practice question
Which expression is equivalent to (x² + 1)(x² − 1)?
- A. x⁴ − 1Correct
- B. x⁴ + 1
- C. x⁴ − 2x² − 1
- D. x² − 1
Answer: A. x⁴ − 1
This is a difference of squares with x² as the 'x': (x²)² − 1² = x⁴ − 1.
Why the other answers are wrong
- B. x⁴ + 1
- The constant is 1 × (−1) = −1, not +1.
- C. x⁴ − 2x² − 1
- The cross terms +x² and −x² cancel; there is no −2x².
- D. x² − 1
- x² − 1 is only one of the factors.
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