Binomials can be factored in several ways, which are factoring out the greatest common factor, finding the difference of squares, using addition to find the sum of cubes or using subtraction to find the difference of cubes. These techniques use different approaches to achieve the same result, which is reducing binomials to their simplest terms. The various methods are used for different types of binomials to correctly solve the equation.
The first technique, which is finding the difference of squares, is most valuable when used in binomials whose integers are perfect squares. These binomials typically have the same sign as well, which may be a plus or minus sign to indicate whether the binomial is negative or positive. Factoring binomials by finding the difference of squares creates two terms, which are often enclosed in parentheses or brackets. Once set up, the product of the two terms can be derived by factoring. The technique of finding the sum of cubes is employed when binomials have roots or numbers with numbers that must be cubed to find their lowest term. The factors in these equations may have multiple terms, which typically follow a pattern. This pattern is a first factor of X+Y, and allows for the terms of all factors to be reduced.