Factor out the common factor:

−3x^4 y^2 + 18xy^3 + 9xy^4

I see the highest common factor as

-3xy^2
I am sure you can write it in factored form.

To factor out the common factor from the given expression, −3x^4y^2 + 18xy^3 + 9xy^4, we need to find the greatest common factor (GCF) of all the terms.

Step 1: Identify the common factors of all terms.

The common factors of −3x^4y^2, 18xy^3, and 9xy^4 are:
-3 (from the coefficient -3),
x (from the variable x),
y^2 (from the variable y, with the smallest exponent of 2).

Step 2: Determine the GCF.

To find the GCF, take the product of the common factors identified in Step 1. In this case, the GCF is -3xy^2.

Step 3: Factor out the GCF.

To factor out the common factor, divide each term by the GCF.

(-3x^4y^2 + 18xy^3 + 9xy^4) / (-3xy^2) = x^3 - 6y + 3y^2

Therefore, the factored form of the given expression is x^3 - 6y + 3y^2.