How do you factor a3+b3 ?

To factor the expression a³ + b³, you can use the sum of cubes formula. The sum of cubes formula is:

a³ + b³ = (a + b)(a² - ab + b²)

Here’s how to derive and understand this formula step-by-step:

Recognize the formula: The general formula for factoring a sum of cubes is: a³ + b³ = (a + b)(a² - ab + b²)

Understand the terms:

(a + b) is the first factor.
(a² - ab + b²) is the second factor.
Example: Let’s apply this formula to an example: Factor a³ + b³.

By the sum of cubes formula, it becomes: (a + b)(a² - ab + b²)

So, the factored form of a³ + b³ is (a + b)(a² - ab + b²).

This is the complete factorization.