What is the formula for a^3 + b^3? Definition, Types, Examples & Uses

What is the formula for a^3 + b^3?

Subject: Mathematics

Book: Algebraic Identities

The sum of cubes of two variables (a^3 + b^3) can be factorized using the following algebraic identity:

(a^3 + b^3) = (a + b)(a^2 - ab + b^2)

### Key Points:
1. **Expansion**: When expanded, (a + b)(a^2 - ab + b^2) reconverts to a^3 + b^3.
2. **Complementary Formula**: The difference of cubes identity is:

(a^3 - b^3) = (a - b)(a^2 + ab + b^2)

3. **Usage**: These sum and difference of cubes formulas are essential for factorizing polynomials, simplifying algebraic expressions, and solving higher-level algebra problems.

Remembering this simple formula helps in quickly dealing with cubic expressions in algebraic contexts.