When factored completely 4x^2y-8x^2y^2=2xy(2x-4xy+3y)
4X^2Y - 8X^2Y^2 = 4X^2Y(1 - 2Y).
To factor the expression 4x^2y - 8x^2y^2 completely, we can follow these steps:
Step 1: Look for the greatest common factor (GCF) among the terms. In this case, both terms have a common factor of 4xy. So we can factor out 4xy from both terms:
4x^2y - 8x^2y^2 = 4xy(x - 2xy)
Step 2: Now, let's look at the expression (x - 2xy). It cannot be factored any further since there are no common factors apart from 1. So our factored expression becomes:
4x^2y - 8x^2y^2 = 4xy(x - 2xy)
Therefore, the completely factored expression is 4xy(x - 2xy).