Answer:
The difference of two cubes is a factorization pattern in algebra. It states that:
a³ - b³ = (a - b)(a² + ab + b²)
Explanation:
- a³ - b³: Represents the difference of two cubes, where 'a' and 'b' are any algebraic expressions.
- (a - b): Represents the difference of the cube roots of the two terms.
- (a² + ab + b²): Represents the sum of the squares of the cube roots and the product of the cube roots.
Example:
Let's factor the expression x³ - 8:
1. Identify 'a' and 'b':
- a = x (cube root of x³)
- b = 2 (cube root of 8)
2. Apply the formula:
- x³ - 8 = (x - 2)(x² + 2x + 4)
Therefore, the factored form of x³ - 8 is (x - 2)(x² + 2x + 4).
