FACTOR OUT: -8x^3y

-32x^5y^4-24x^4y-16x^3y=

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To factor out -8x^3y from the expression -32x^5y^4 - 24x^4y - 16x^3y, follow these steps:

Step 1: Find the common factors
Look for the highest power of each variable that appears in all terms. In this case, the variables are x and y. The highest power of x that appears in all terms is x^3, and the highest power of y that appears in all terms is y. The common factor of x^3y is -8x^3y since it can be factored out of each term.

Step 2: Divide each term by the common factor
Divide each term by -8x^3y:

-32x^5y^4 / (-8x^3y) = 4x^2y^3
-24x^4y / (-8x^3y) = 3xy
-16x^3y / (-8x^3y) = 2

Step 3: Write the factored form
Now that we have divided each term by the common factor, we can express the original expression as the product of -8x^3y and the resulting terms we obtained in the previous step:

-32x^5y^4 - 24x^4y - 16x^3y = -8x^3y(4x^2y^3 + 3xy + 2)

Therefore, the factored form of -32x^5y^4 - 24x^4y - 16x^3y is -8x^3y(4x^2y^3 + 3xy + 2).