Advanced MathEasy–MediumSquaring a binomial in two variables
Advanced Math practice question
Which expression is equivalent to (x − 3y)²?
- A. x² − 6xy + 9y²Correct
- B. x² + 9y²
- C. x² − 9y²
- D. x² − 3xy + 9y²
Answer: A. x² − 6xy + 9y²
(x − 3y)(x − 3y) = x² − 3xy − 3xy + 9y² = x² − 6xy + 9y².
Why the other answers are wrong
- B. x² + 9y²
- The middle term is missing. Squaring a binomial always produces a cross term, here −6xy.
- C. x² − 9y²
- x² − 9y² is (x − 3y)(x + 3y), a difference of squares — not a square of a binomial.
- D. x² − 3xy + 9y²
- The cross term −3xy appears twice, so it doubles to −6xy.
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For x ≠ 0, which expression is equivalent to (x² + 3x) / x? - Easy–Medium
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