This thread is derailing.
Sums and Differences of Cubes
When you have a binomial where each term is the cube of something, such as x3 - 27, there are formulas that you can apply to the binomial so you don't have to factor them. The two formulas are listed below.
1. Sum of Cubes
A3 + B3 = (A + B)(A2 - AB + B2)
2. Difference of Cubes
A3 - B3 = (A - B)(A2 + AB + B2
Use the formulas whenever you can! Example:
1. Problem: Factor 125x3 + y3.
Solution: Write the sum of the cube roots.
(5x + y)( )
Take 5x + y to get the next factor.
Think of the Sum of Cubes formula
(A + B)(A2 - AB + B2).
5x would be A and y would
be B.
(5x + y)(25x2 - 5xy + y2)