Factor completely with the GCF. 27x ^(2) y - 42x {}^(2) y ^(2) A. xy(27x – 42xy) B. x^2y(27 – 42) C. 3xy(9x – 14xy) D. 3x^2y(9 – 14y)​

Question

Factor completely with the GCF.


`27x ^(2) y - 42x {}^(2) y ^(2)`

A. xy(27x – 42xy)


B. x^2y(27 – 42)


C. 3xy(9x – 14xy)


D. 3x^2y(9 – 14y)​

Answer 1

D. 3x^2y(9 – 14y)​

Explanation:

To factor the expression 27x^2y - 42x^2y^2 completely using the greatest common factor (GCF) method, we need to find the largest common factor that can be factored out from both terms.

First, let's identify the common factors of the coefficients 27 and 42. The prime factorization of 27 is 3 * 3 * 3, and the prime factorization of 42 is 2 * 3 * 7. The common factor between them is 3.

Next, let's look at the variables. We have x^2 and y as common variables in both terms. The lowest exponent of x is 2, and the lowest exponent of y is 1.

Therefore, the GCF of 27x^2y and 42x^2y^2 is 3x^2y.

Now, we can factor out the GCF from the expression:

27x^2y - 42x^2y^2 = 3x^2y(9 - 14y)

Thus, the factored form of the expression using the GCF is 3x^2y(9 - 14y).