algebra
Sum and difference of cubes — AMC & AIME Problems
21 problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Sum and difference of cubes — a algebra concept — each with a professionally curated solution, many with a video solution too, from LIVE by Po-Shen Loh. Browse all concepts or the full past-contest archive.
LIVE focuses on challenge. As a social enterprise, we also explain standard school concepts one at a time, for free, on our sister site Expii. For this idea: Sums and Differences of Cubes.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
Filter by difficulty
These problems’ difficulty ratings come from real solve attempts on our platform. Tap a band or a contest to filter the list below, and tap a selected band again to include all difficulties. See the full difficulty guide.
AMC 12
- 1951 AMC 12 Problem 40
- 1952 AMC 12 Problem 3
- 1954 AMC 12 Problem 40
- 1963 AMC 12 Problem 40
- 1966 AMC 12 Problem 10
- 1972 AMC 12 Problem 34
- 1975 AMC 12 Problem 12
- 1977 AMC 12 Problem 23
- 1980 AMC 12 Problem 27
- 2004 AMC 12A Problem 25
- 2005 AMC 12B Problem 23
- 2009 AMC 12A Problem 18
- 2022 AMC 12A Problem 14
- 2023 AMC 12A Problem 12
More algebra concepts
- Absolute value
- Ages
- Algebraic manipulation
- AM-GM Inequality
- Arithmetic sequence
- Arithmetico-geometric series
- Binomial theorem
- Calculus
- Cauchy-Schwarz Inequality
- Completing the square
- Complex number
- Custom operation
- De Moivre’s Theorem
- Determinant
- Difference of squares
- Factoring
- Fibonacci
- Floor and ceiling functions
- Function
- Functional equation
- Geometric sequence
- Inequality
- Linear equation
- Logarithm
- Matrix
- Mixture
- Newton’s Sums
- Partial fractions
- Polynomial
- Quadratic
- Radical
- Rational equation
- Rationalizing denominator
- Recursion
- Roots of unity
- Simon’s Favorite Factoring Trick
- Slope
- Substitution
- Sum of first n cubes
- Sum of first n odd numbers
- Sum of first n squares
- Summation
- Symmetry (algebra)
- System of equations
- Telescoping
- Vieta’s Formulas
- Zero product property