Note the following cube root calculations
The cube root of the first term x3 = x ← This is {a}The cube root of the second term 27y9 = 3y3 ← This is {b}
Since both cube roots are integer constants and powers, x3 - 27y9 is in the Difference of cubes format
The formula for factoring the Difference of cubes is as follows:
a3 - b3 = (a - b)(a2 + ab + b2)Calculate ab
ab = (x)(3y3)ab = (1 x 3)xy3
ab = 3xy3
Calculate the square of the a term:
The square of the a term = (x)2 = x(1 x 2)The square of the a term = (x)2 = x2
Calculate the square of the b term:
The square of the b term = (3y3)2 = 32y(3 x 2)The square of the b term = (3y3)2 = 9y6
Our factored expression using the Difference of cubes formula becomes:
(x - 3y3)(x2 + 3xy3 + 9y6)Our factored out term becomes:
(x - 3y3)(x2 + 3xy3 + 9y6)
Common Core State Standards In This Lesson
HSA.SSE.A.2, HSA.APR.B.3
What is the Answer?
(x - 3y3)(x2 + 3xy3 + 9y6)
How does the Factoring and Root Finding Calculator work?
Free Factoring and Root Finding Calculator - This calculator factors a binomial including all 26 variables (a-z) using the following factoring principles:
* Difference of Squares
* Sum of Cubes
* Difference of Cubes
* Binomial Expansions
* Quadratics
* Factor by Grouping
* Common Term
This calculator also uses the Rational Root Theorem (Rational Zero Theorem) to determine potential roots
* Factors and simplifies Rational Expressions of one fraction
* Determines the number of potential positive and negative roots using Descarte’s Rule of Signs
This calculator has 1 input.
* Difference of Squares
* Sum of Cubes
* Difference of Cubes
* Binomial Expansions
* Quadratics
* Factor by Grouping
* Common Term
This calculator also uses the Rational Root Theorem (Rational Zero Theorem) to determine potential roots
* Factors and simplifies Rational Expressions of one fraction
* Determines the number of potential positive and negative roots using Descarte’s Rule of Signs
This calculator has 1 input.
What 3 formulas are used for the Factoring and Root Finding Calculator?
a2 - b2 = (a + b)(a - b)
a3 + b3 = (a + b) (a2 - ab + b2)
a3 - b3 = (a - b) (a2 + ab + b2)
a3 + b3 = (a + b) (a2 - ab + b2)
a3 - b3 = (a - b) (a2 + ab + b2)
What 5 concepts are covered in the Factoring and Root Finding Calculator?
- factor
- a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n.
- polynomial
- an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).
- rational expressions
- Quotient of two polynomials
P(x)/Q(x) - rational root theorem
- used to find the rational solutions of a polynomial equation
- rational zero theorem
- used to find the rational roots of a polynomial function
