Advanced MathVery hardDifference of two cubes of binomials
Advanced Math practice question
The expression (x + 2)³ − (x − 2)³ is equivalent to ax² + b, where a and b are constants. What is the value of a + b?
Answer: 28
(x + 2)³ = x³ + 6x² + 12x + 8 and (x − 2)³ = x³ − 6x² + 12x − 8. Subtracting, the x³ and 12x terms cancel: 12x² + 16. So a + b = 12 + 16 = 28.
Common wrong answers
- If you answered 0
- 0 comes from assuming everything cancels; the x² and constant terms double rather than cancel.
- If you answered 12
- 12 is a alone.
- If you answered 16
- 16 is b alone.
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