Advanced MathHardConstant in a simplified difference
Advanced Math practice question
For all values of x, (x + 3)² − (x − 1)(x + 1) = ax + b, where a and b are constants. What is the value of a + b?
Answer: 16
(x + 3)² = x² + 6x + 9 and (x − 1)(x + 1) = x² − 1. Subtract: 6x + 10, so a = 6, b = 10, and a + b = 16.
Common wrong answers
- If you answered 6
- 6 is a alone.
- If you answered 10
- 10 is b alone.
- If you answered 14
- 14 comes from x² + 6x + 9 − x² + 1 miscounted as 6x + 8 (subtracting the 1 instead of adding it).
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