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2020 Math Kangaroo

Problem 4

Problem 4 · 2020 Math Kangaroo Medium
Algebra & Patterns substitution

What is the value of \(1010^3 - 2020^3 + 3030^3\)\(1010^3\)?

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Answer: B — 20
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Hint 1 of 2
Notice 1010, 2020, 3030 are 1, 2, 3 times the same number.
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Hint 2 of 2
Factor 1010³ out of every term.
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Approach: factor out the common cube
  1. Let x = 1010, so 2020 = 2x and 3030 = 3x.
  2. Numerator = x³(1 − 8 + 27) = 20x³.
  3. Divide by x³ to get 20.
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