This free Factoring Binomials as Sum or Difference of Cubes Calculator tool is useful to find the factors of binomials using the sum or difference of cubes method. All you have to do is enter the expression in the input box and press the calculate button to avail the output in a short span of time
Sum and Difference of Cubes - Definition, Formulas
Sum and difference of cubes is a method that is used to find the factors of polynomials. A cube of a binomial is an expression that is multiplied itself by three times. The expression in the form of x³ + y³ is called the sum of two cubes as two cubic terms are added together. The polynomial in the form of x³ - y³ is called the difference of two cubes as cubic terms are being subtracted..
Sum of Two Cubes:
X³ + y³ = (x + y)(x² - xy + y²)
a^3 + b^3 = (a + b)(a^2 – ab + b^2)
Difference of Two Cubes:
X³ - y³ = (x - y)(x² + xy + y²)
How to Factor Binomials Using Sum or Difference of Cubes?
Apply one of the factoring formula to find the factors of polynomials using sum or difference of cubes. The simple steps to solve the factoring binomials questions are listed here:
- Find wither the given polynomials have sum or difference.
- Convert the polynomials into sum or difference of cubes
- Substitute the values in the required formula and solve.
- Finally the exact factors are obtained.
Factoring Binomials as sum or difference of cubes with Example
Question: Find factors of 8m³ - 125l³?
Given expression is 8m³ - 125l³
The expression is difference of cubes
8m³ - 125l³ = (2m)³ - (25l)³
The difference of cubes formula is X³ - y³ = (x - y)(x² + xy + y²)
So, (2m)³ - (25l)³ = (2m - 5l)((2m)² + (2m)(5l) + (5l)²)
= (2m - 5l)(4m² -10ml + 25l²)
Therefore, 8m³ - 125l³ = (2m - 5l)(4m² -10ml + 25l²)
FAQs on Factoring Binomials as Sum or difference of cubes Calculator
1. How do you factor the sum or difference of cubes?
To factor the sum or difference of cubes, you have to convert the given polynomial in the form of a³ + b³ or a³ - b³. Using those formulas, you can get the result.
2. What is the rule for cubing a sum of binomials?
The cubing of a binomial is defined as the multiplication of a binomial 3 times itself. The sum of binomial expression is in the form of a + b. So, the cube of the binomial is expressed as (a + b) (a + b) (a + b) = (a + b)³. Therefore, the rule for cubing a binomial should be either in the form of a³ + b³ or (a + b)³. Its formula is (a + b)³ = a³ + b³ + 3ab.
3. What is the definition of factorisation of polynomials?
The process of finding the multiples of a polynomial or factoring is called factorisation of polynomials.
4. What is the sum and difference of binomial?
In binomial products of the form (a + b) and (a - b), (a + b) is called sum and (a - b) is called difference. So in every polynomial, if there is + between variables is sum, otherwise difference of binomial.
5. What are different methods of factoring?
The different methods used to factorise polynomials are greatest common factor (GCF), grouping method, difference in two squares method, sum or difference in two cubes, general trinomials and trinomial method.