factor out the GFC for each

Question

-4x^y + 12xy^2

-16x^3y^2 + 8x^2y^3 - 16x^4y (wrong answer)

Answer 1

For the first expression, -4x^y + 12xy^2, the greatest common factor (GCF) is 4xy. Factoring out 4xy gives us:

4xy(-x + 3y)

For the second expression, -16x^3y^2 + 8x^2y^3 - 16x^4y, the greatest common factor (GCF) is 8x^2y. Factoring out 8x^2y gives us:

8x^2y(-2xy + y^2 - 2x^2)

Answer 2

factor out the GFC
-16x^3y^2 + 8x^2y^3 - 16x^4y

Answer 3

To factor out the greatest common factor (GCF) of the expression -16x^3y^2 + 8x^2y^3 - 16x^4y, we first need to identify the terms that have common factors.

The terms in the expression are:
-16x^3y^2
8x^2y^3
-16x^4y

Let's find the common factors of these terms:

-16x^3y^2 can be rewritten as -16x^3y * y.
8x^2y^3 can be rewritten as 8x^2 * y^2.
-16x^4y can be rewritten as -16x^3 * x * y.

The common factor between all three terms is 8x^2y.

Therefore, the factored form of the expression -16x^3y^2 + 8x^2y^3 - 16x^4y with the GCF factored out is:
8x^2y(-2y + y^2 - 2x)