How do you factor the difference of two perfect cubes?
Factoring completely is a three step process:
- Factor a GCF from the expression, if possible.
- Factor a Trinomial, if possible.
- Factor a Difference Between Two Squares as many times as possible.
What is the perfect cube factor?
To factor the expression, we do the following:
- We determine what the a and b for our formula are. The first term is easy, x is the a. ...
- Then, we substitute those values into the formula: ( x + 4) ( x ^2 - ( x ) (4) + 4^2).
- We can rewrite the ( x ) (4) as 4 x, and evaluate the exponent in the last term to clean it up. ...
How to Cube a number easily and quickly?
How to Cube a Number easily and quickly The cube of a number is that number multiplied by itself twice. For example, 5 cubed - denoted as 5 3; is equal to 5×5×5 = 125. The technique for cubing any 2-digit number discussed below is based on the algebraic observation.
What is the easiest way to factor a cubic polynomial?
- Say we're working with the polynomial x3 + 3x2 - 6x - 18 = 0. Let's group it into (x3 + 3x2) and (- 6x - 18)
- Find what's the common in each section.
- Looking at (x3 + 3x2), we can see that x2 is common.
- Looking at (- 6x - 18), we can see that -6 is common.
- Factor the commonalities out of the two terms.
- Factoring out x2 from the first sectio
Can you factor cubes?
To factor a sum of cubes, find a and b and plug them into (a + b)(a2 - ab + b2).
Is there a difference of cubes?
Sum or Difference of Cubes A polynomial in the form a 3 + b 3 is called a sum of cubes. A polynomial in the form a 3 – b 3 is called a difference of cubes.
How do you factor the difference of two cubes?
0:005:53Factoring Sums and Differences of Cubes - YouTubeYouTubeStart of suggested clipEnd of suggested clipAnd there's two formulas you've got to know the first one says if you have something cubed minusMoreAnd there's two formulas you've got to know the first one says if you have something cubed minus something cubed you get the quantity. So X cubed minus y cubed we get the quantity X minus y.
Is there a difference of two cubes?
The sum or difference of two cubes can be factored into a product of a binomial times a trinomial. That is, x3+y3=(x+y)(x2−xy+y2) and x3−y3=(x−y)(x2+xy+y2) .
How to find the difference of cubes?
Step 2: Substitute the values found for a and b into the difference of cubes factoring formula {eq}a^3 - b^3 = (a-b) (a^2 + ab +b^2) {/eq}.
What is factoring in math?
Factoring: Factoring is the process of undoing distribution. Factoring is useful in finding the roots of equations. We will use these steps and definitions to factor a difference of cubes in the following two examples. One example will only involve variables and integers and the other example will also include fractions.
How to factor a difference of cubes?
To factor a difference of cubes, we can follow the following steps: Step 1: Decide if the two terms have a common factor, called the greatest common factor. If so, we factor the greatest common factor from the expression. We must not forget to include the greatest common factor as part of the final answer.
Examples with answers of factoring a difference of cubes
The following difference of cubes factoring examples use the solving process listed above. Each exercise has a detailed solution that helps to understand the reasoning used to obtain the answer.
Factoring difference of cubes – Exercises to solve
Test what you have learned about factoring difference of cubes with the following exercises. Solve the exercises and choose an answer. Check the selected answer to see if it is correct.
How to factor the difference between two perfect cubes?
To factor the two perfect cubes differences, remember that the difference of two perfect cubes equals the variance of their cube roots calculated by the product of their cube roots and the sum of their squares.
What is the difference of cubes in algebra?
The difference of cubes formula in algebra is used to calculate the value of the algebraic expression (a³ - b³). In simplistic words, it is applied to equate the difference of two cube values. Therefore the Formula for Difference of Cubes in Algebra is given as:
What is the difference between two cubes?
The difference between the two cubes is equal to the difference of their cube roots, which contains the cube roots' squares and the opposite of the cube roots' product.
How to factor the sum of two cubes?
Answer : To factor the sum of two cubes, determine if the two terms have the greatest common factor or GCF. Next, rewrite the first problem as a difference of two perfect cubes, then use those three pieces to write the final answer.
What are the two criteria for factoring?
Answer : An expression requires two criteria to be factored as a sum of cubes. First, each term must be a cube. Secondly, each term should have the same sign, usually both positive.
Factoring A Difference of Cubes
Factoring A Difference of Cubes - Vocabulary
- Difference of Cubes:A difference of cubes is two perfect cube terms with subtraction in between. A perfect cube can be written as a term multiplied by itself a total of three times. Factoring:Factoring is the process of undoing distribution. Factoring is useful in finding the roots of equations. We will use these steps and definitions to factor a d...
Example Problem 1: Factoring A Difference of Cubes - Integers and Variables
- Factor the expression. {eq}125x^3 - y^3{/eq} Step 1: Determine the values of a and bin the difference of cubes {eq}a^3 - b^3{/eq}. Since {eq}125 = 5\cdot 5\cdot 5 = 5^3{/eq}, we can rewrite our expression as: {eq}125x^3 - y^3 = (5x)^3 - y^3{/eq} Then, in the difference of cubes, a = 5x and b = y. Step 2: Substitute the values found for a and binto the difference of cubes factoring formu…
Example Problem 2: Factoring A Difference of Cubes - Fractions
- Factor the expression. {eq}\dfrac{p^3}{8} - \dfrac{216}{343}{/eq} Step 1: Determine the values of a and bin the difference of cubes {eq}a^3 - b^3{/eq}. Since {eq}8=2^3{/eq}, {eq}216 = 6^3{/eq}, and {eq}343 = 7^3{/eq}, we can rewrite our expression as: {eq}\dfrac{p^3}{8} - \dfrac{216}{343} = \left(\dfrac{p}{2}\right)^3 - \left(\dfrac{6}{7}\right)^3{/eq} Then, in the difference of cubes, {eq}a …
How to Factor A Difference of Cubes?
Factoring A Difference of Cubes – Examples with Answers
- The following difference of cubes factoring examples use the solving process listed above. Each example has a detailed solution that helps to understand the reasoning used to obtain the answer. Start now: Explore our additional Mathematics resources
Factoring Difference of Cubes – Practice Problems
- Test what you have learned about factoring the difference of cubes with the following problems. Solve the exercises and choose an answer. Check the selected answer to see if it is correct.
See Also
- Interested in learning more about the factorization of polynomials? Take a look at these pages: 1. Factoring Polynomials Calculator 2. Factoring Quadratic Equations with Examples 3. Factoring Binomials Cubed 4. Examples of Factoring Trinomials 5. Examples of Perfect Square Trinomial