Advanced MathHardSquaring a difference with a reciprocal term
Advanced Math practice question
For x ≠ 0, which expression is equivalent to (2x − 3/x)²?
- A. 4x² − 12 + 9/x²Correct
- B. 4x² + 9/x²
- C. 4x² − 6 + 9/x²
- D. 4x² − 12x + 9/x²
Answer: A. 4x² − 12 + 9/x²
(2x − 3/x)² = (2x)² − 2(2x)(3/x) + (3/x)² = 4x² − 12 + 9/x², because 2x · 3/x = 6 and doubling it gives 12.
Why the other answers are wrong
- B. 4x² + 9/x²
- The middle term is missing. Squaring a binomial produces a cross term: −2(2x)(3/x) = −12.
- C. 4x² − 6 + 9/x²
- The cross term is doubled: 2 × (2x)(3/x) = 12, not 6.
- D. 4x² − 12x + 9/x²
- In 2x · 3/x the x's cancel, so the middle term is a constant −12, not −12x.
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