Final answer:
The Greatest Common Factor (GCF) of the expression 2y^2 - 8xy^3 is 2y^2. After factoring out the GCF, the expression becomes 2y^2(1 - 4xy).
Step-by-step explanation:
To factor out the Greatest Common Factor (GCF) in the expression 2y2 - 8xy3, we first need to identify the common factors in each term.
Look at the coefficients: The GCF of 2 and 8 is 2.
Now examine the variables: The GCF for y2 and y3 is y2 because it is the highest power of y that is present in both terms.
The variable x is only present in the second term, so it is not part of the GCF.
Factoring out the GCF:
Divide each term by 2y2.
Write the expression as the product of the GCF and the remaining terms.
The factored expression is 2y2(1 - 4xy).