What is the formula for the difference of cubes?

The difference of cubes formula is expressed as ( a^3 - b^3 = (a - b)(a^2 + ab + b^2) ). This formula is derived from the properties of polynomial factoring and can be understood as follows:

When you have the expression ( a^3 - b^3 ), it represents the difference between two cubes. By factoring it, you break it down into two parts: the linear factor ( (a - b) ), which corresponds to the difference of the bases (in this case, ( a ) and ( b )), and the quadratic factor ( (a^2 + ab + b^2) ), which accounts for the relationship between the cubes of the two numbers.

To confirm this formula, consider that if you expand the right side, it should return you to the original cubic expression:

1. Multiply ( (a - b) ) by ( (a^2 + ab + b^2) ).

2. Distributing results in:

• ( a \cdot a^2 = a^3 )

• ( a \cdot ab = a^2b )

• ( a \cdot b^2 =