SUMMARY
The expression (a + b)^3 - 8c^3 can be simplified using the difference of cubes formula, which states that x^3 - a^3 = (x - a)(x^2 + ax + a^2). By letting x = (a + b) and a = 2c, the expression becomes (a + b - 2c)((a + b)^2 + 2c(a + b) + 4c^2). The key insight is recognizing that 8c^3 can be rewritten as (2c)^3, allowing for the application of the difference of cubes formula.
PREREQUISITES
- Understanding of algebraic identities, specifically the difference of cubes.
- Familiarity with polynomial expressions and factoring techniques.
- Knowledge of exponential properties, particularly how to manipulate bases and exponents.
- Basic skills in algebraic manipulation and simplification.
NEXT STEPS
- Study the difference of cubes formula in detail, including various examples.
- Practice factoring polynomial expressions using different algebraic identities.
- Learn about exponential properties and their applications in algebra.
- Explore advanced factoring techniques for higher-degree polynomials.
USEFUL FOR
Students, educators, and anyone involved in algebra who seeks to deepen their understanding of polynomial factoring and the application of algebraic identities.