Factor x^3-27y^9
Factor x3 - 27y9Note 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)
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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
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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)
For more math formulas, check out our Formula Dossier
What 5 concepts are covered in the Factoring and Root Finding Calculator?
factora 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.polynomialan expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).rational expressionsQuotient of two polynomialsP(x)/Q(x)rational root theoremused to find the rational solutions of a polynomial equationrational zero theoremused to find the rational roots of a polynomial function
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