Factor 9x^2-4y^2

corga
Image to Crop Factor 9x2 - 4y2

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)


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.

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 polynomials
P(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

Example calculations for the Factoring and Root Finding Calculator

Factoring and Root Finding Calculator Video


Tags:

Add This Calculator To Your Website

ncG1vNJzZmivp6x7rq3ToZqepJWXv6rA2GeaqKVfm66kwM6rZamgoHTBpr7ManRysFVqknN5k7Jcbn1iW72tiaWamq2nog%3D%3D