factor out the greatest common factor from the expression
6x^3yz^4-3x^2y^3z^4-18^4y^2z^3
Assuming you meant
6x^3yz^4 - 3x^2y^3z^4 - 18x^4y^2z^3,
3x^2yz^3(2xz- y^2z - 6x^2y)
To factor out the greatest common factor from the expression 6x^3yz^4 - 3x^2y^3z^4 - 18^4y^2z^3, we need to identify the factors that all terms share in common.
First, let's break down each term into its factors:
6x^3yz^4 can be expressed as (2 * 3) * (x * x * x) * y * z * z * z * z.
3x^2y^3z^4 can be expressed as (3) * (x * x) * (y * y * y) * z * z * z * z.
18^4y^2z^3 can be expressed as (2 * 3 * 3) * (2 * 3 * 3) * (2 * 3 * 3) * y * y * z * z * z.
Next, let's identify the common factors:
The numbers 2, 3, y, z, and z^3 are factors that all terms share.
Now, let's find the power of each common factor:
The highest power of x common to all terms is x^2 (from the second term).
The highest power of y common to all terms is y (from all three terms).
The highest power of z common to all terms is z^3 (from the first and third terms).
Therefore, we can factor out the expression by taking the product of the common factors and their highest powers:
The greatest common factor is 2 * 3 * y * z^3 = 6yz^3.
Factoring out the greatest common factor, we get:
6yz^3(x^3z - x^2y^2z - 3^2yz).
Thus, the expression 6x^3yz^4 - 3x^2y^3z^4 - 18^4y^2z^3 can be factored as 6yz^3(x^3z - x^2y^2z - 3^2yz).