Advanced MathVery hardSlope of a linear difference of squares
Advanced Math practice question
The graph of y = (x + 6)² − (x − 6)² in the xy-plane is a line. What is its slope?
Answer: 24
(x² + 12x + 36) − (x² − 12x + 36) = 24x: a line through the origin with slope 24.
Common wrong answers
- If you answered 0
- 0 would mean the squares were equal, which is false unless x = 0.
- If you answered 12
- 12 halves the answer; the middle terms are +12x and −12x, which combine to 24x.
- If you answered 72
- 72 is the sum of the constants 36 + 36, but they cancel.
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