The sum of the cubes of two expressions is equal to the product of the sum of the first and the second expressions and the incomplete square of the difference of these expressions.

In other words, the sum of the cubes is the product of the two brackets: in the first bracket – the sum of two expressions, in the second bracket – the incomplete square of the difference.

 

The sum of the cubes of two expressions  

 

 The incomplete square of the difference of two numbers is an expression, which differs from the perfect square by the fact that it has the product of two numbers in the middle rather than twice the product of these numbers:

The incomplete square of the difference of two numbers

Or

The product of the sum of two expressions and the incomplete square of the difference is equal to the sum of their cubes:

 

The sum of the cubes of two expressions

Derivation of the formula

Derivation of the formula