Expansion formulas

This is a list of expansion formulas, which are used to expand algebraic expressions that follow a certain pattern. These formulas help in factoring algebraic expressions when they are used the opposite way.


Click on the links to each formula's individual web page, so that you get to see an example of how it works, forwards and backwards.

Difference of two squares:

a² - b² = (a + b)(a - b)

Square of a sum:

(a + b)² = a² + b² + 2ab

Square of a difference:

(a - b)² = a² + b² - 2ab

Sum of cubes:

a³ + b³ = (a + b)(a² - ab + b²)

Difference of cubes:

a³ - b³ = (a - b)(a² + ab + b²)

Cube of a sum:

(a + b)³ = a³ + b³ + 3ab(a + b)

Cube of a difference:

(a - b)³ = a³ - b³ - 3ab(a - b) 

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Greatest Common Divisor (GCD)Next:
Solved Examples on Factoring in Algebra