Problem 2 · 2015 Math Kangaroo
Easy
Algebra & Patterns
substitution
(a − b)3 + (b − a)3 =
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Answer: A — 0
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Hint 1 of 2
Notice that b−a is just the opposite of a−b.
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Hint 2 of 2
Cubing an opposite flips the sign.
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Approach: use that (b−a) = −(a−b)
- Since b−a = −(a−b), we get (b−a)³ = −(a−b)³.
- The two cubes cancel: (a−b)³ + (b−a)³ = 0 (A).
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