Consider the monomials 15x^2y^2 and 6x^3y.
a. Factor the monomials.
b. What factors of these monomials are common factors?
c. Find the greatest common factor of 15x^2y^2 and 6x^3y.
(UPDATED VER.)
15x^2y^2 = 3*5*x*x*y*y
6x^3y = 2*3*x*x*x*y
I see a 3 common to both of them
a pair of x's common to both of them
a single y common to both of them, so .......
Thank you so much!
a. To factor the monomials:
The first monomial, 15x^2y^2, is already fully factored.
The second monomial, 6x^3y, can be factored as 2 * 3 * x * x * x * y.
b. The factors of these monomials are:
15x^2y^2: 1, 3, 5, 15, x, x, y, y
6x^3y: 1, 2, 3, 6, x, x, x, y
c. To find the greatest common factor (GCF), we look for the factors that both monomials have in common.
The common factors between 15x^2y^2 and 6x^3y are: 1, 3, x, x, y.
To find the greatest common factor, we take the product of the common factors:
GCF = 1 * 3 * x * x * y = 3x^2y
Therefore, the greatest common factor of 15x^2y^2 and 6x^3y is 3x^2y.
To factor the monomials 15x^2y^2 and 6x^3y:
a. Factor the first monomial, 15x^2y^2:
The number 15 can be factored into 5 and 3.
The variable x^2 represents x * x, and y^2 represents y * y.
Therefore, the factored form of 15x^2y^2 is 5 * 3 * x * x * y * y, or 15x^2y^2.
Now, let's factor the second monomial, 6x^3y:
The number 6 can be factored into 2 and 3.
The variable x^3 represents x * x * x, and there's already a single y.
Thus, the factored form of 6x^3y is 2 * 3 * x * x * x * y, or 6x^3y.
b. The common factors of these monomials are the factors that appear in both of their factored forms. Looking at the factored forms, we can see that the common factors are: 3, x, and y.
c. To find the greatest common factor (GCF) of 15x^2y^2 and 6x^3y, we simply multiply the common factors we found in part b: 3 * x * y.
Therefore, the GCF of 15x^2y^2 and 6x^3y is 3xy.