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:

aSquare of a sum:^{2}- b^{2}= (a + b)(a - b)

(a + b)Square of a difference:^{2}= a^{2}+ b^{2}+ 2ab

(a - b)Sum of cubes:^{2}= a^{2}+ b^{2}- 2ab

aDifference of cubes:^{3}+ b^{3}= (a + b)(a^{2}- ab + b^{2})

aCube of a sum:^{3}- b^{3}= (a - b)(a^{2}+ ab + b^{2})

(a + b)Cube of a difference:^{3}= a^{3}+ b^{3}+ 3ab(a + b)

(a - b)^{3}= a^{3}- b^{3}- 3ab(a - b)