Problem 4 · 2020 Math Kangaroo
Medium
Algebra & Patterns
substitution
What is the value of \(1010^3 - 2020^3 + 3030^3\)\(1010^3\)?
Show answer
Answer: B — 20
Show hints
Hint 1 of 2
Notice 1010, 2020, 3030 are 1, 2, 3 times the same number.
Still stuck? Show hint 2 →
Hint 2 of 2
Factor 1010³ out of every term.
Show solution
Approach: factor out the common cube
- Let x = 1010, so 2020 = 2x and 3030 = 3x.
- Numerator = x³(1 − 8 + 27) = 20x³.
- Divide by x³ to get 20.
Mark:
· log in to save