factor out the GFC for each
-4x^y + 12xy^2
-16x^3y^2 + 8x^2y^3 - 16x^4y (wrong answer)
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)
factor out the GFC
-16x^3y^2 + 8x^2y^3 - 16x^4y
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)