Note the following square root calculations
The square root of the first term is denoted below:
Square Root of the Constant Piece = √9 = 3
Square Root of the Variable Piece (Divide exponents by 2) = x2÷2 = x
Our final square root term becomes 3x
The square root of the second term 4y2 is denoted below:
Square Root of the Constant Piece = √4 = 2
Square Root of the Variable Piece (Divide exponents by 2) = y2÷2 = y
Our final square root term becomes 2y
Since both square roots are integer constants and powers, 9x2 - 4y2 is in the difference of squares format
The formula for factoring the difference of squares is as follows:
a2 - b2 = (a - b)(a + b)In the expression you entered, the {a} term is 3x and the {b} term is 2y
Our factored expression using the difference of squares becomes:
(3x + 2y)(3x - 2y)Our factored out term becomes:
(3x + 2y)(3x - 2y)
Common Core State Standards In This Lesson
HSA.SSE.A.2, HSA.APR.B.3
What is the Answer?
(3x + 2y)(3x - 2y)
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
