Advanced MathHardSquaring a binomial with a square root
Advanced Math practice question
For x ≥ 0, which expression is equivalent to (√x + 2)²?
- A. x + 4√x + 4Correct
- B. x + 4
- C. x + 2√x + 4
- D. x + 4√x + 2
Answer: A. x + 4√x + 4
(√x + 2)² = (√x)² + 2 · √x · 2 + 2² = x + 4√x + 4.
Why the other answers are wrong
- B. x + 4
- x + 4 drops the middle term; a binomial squared always has one.
- C. x + 2√x + 4
- The middle term is 2 · 2 · √x = 4√x, not 2√x.
- D. x + 4√x + 2
- The constant is 2² = 4, not 2.
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