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2015 Math Kangaroo

Problem 2

Problem 2 · 2015 Math Kangaroo Easy
Algebra & Patterns substitution

(ab)3 + (ba)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)
  1. Since b−a = −(a−b), we get (b−a)³ = −(a−b)³.
  2. The two cubes cancel: (a−b)³ + (b−a)³ = 0 (A).
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