A³ - B³ Formula Example
The formula for the difference of cubes is:
a³ - b³ = (a - b)(a² + ab + b²)
This formula allows us to factor a difference of two perfect cubes. Here's how it works:
- a³ represents the first term, which is a cube of a variable or a number.
- b³ represents the second term, which is a cube of a variable or a number.
- (a - b) is the difference of the cube roots of the two terms.
- (a² + ab + b²) is the sum of the squares of the cube roots and their product.
Example:
Let's factor the expression: 8x³ - 27
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Identify a and b:
- a = 2x (cube root of 8x³)
- b = 3 (cube root of 27)
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Apply the formula:
- (2x - 3)((2x)² + (2x)(3) + 3²)
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Simplify:
- (2x - 3)(4x² + 6x + 9)
Therefore, the factored form of 8x³ - 27 is (2x - 3)(4x² + 6x + 9).
Using the formula, you can factor any expression that can be written in the form of a³ - b³.
