Advanced MathHardCoefficient after simplifying a difference
Advanced Math practice question
For all x, (x − 5)(x + 5) − (x − 5)² = ax + b, where a and b are constants. What is the value of a?
Answer: 10
(x − 5)(x + 5) = x² − 25 and (x − 5)² = x² − 10x + 25. Subtract: 10x − 50, so a = 10.
Common wrong answers
- If you answered 0
- 0 would mean the x-terms cancelled; only the x² terms cancel.
- If you answered -10
- −10 has the wrong sign: subtracting (−10x) gives +10x.
- If you answered -50
- −50 is b, not a.
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