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Step-by-step explanation:
To factor the polynomial \(4x^2y - 16xy^2\), follow these steps:
1. **Find the Greatest Common Factor (GCF):**
- For the coefficients: The GCF of 4 and 16 is 4.
- For the \(x\) terms: The GCF of \(x^2\) and \(xy\) is \(x\).
- For the \(y\) terms: The GCF of \(y\) and \(y^2\) is \(y\).
Therefore, the GCF of \(4x^2y\) and \(16xy^2\) is \(4xy\).
2. **Factor out the GCF:**
\[
4x^2y - 16xy^2 = 4xy(x - 4y)
\]
Thus, the factored form of \(4x^2y - 16xy^2\) is \(4xy(x - 4y)\).