Recognize the type of expression and use an appropriate method to factor it completely. $$ 48 y^{3} x^{2}-8 x y^{4} $$

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To factor the expression $$ 48 y^{3} x^{2} - 8 x y^{4} $$ completely, follow these steps:

### 1. Identify the Greatest Common Factor (GCF)
First, determine the GCF of the coefficients and the variables in each term.

- **Coefficients:** The coefficients are 48 and 8.  
  - The GCF of 48 and 8 is **8**.

- **Variables:**
  - For $$ x $$: The terms have $$ x^{2} $$ and $$ x $$.  
    - The GCF is $$ x $$ (since $$ x $$ is the highest power common to both).
  
  - For $$ y $$: The terms have $$ y^{3} $$ and $$ y^{4} $$.  
    - The GCF is $$ y^{3} $$ (since $$ y^{3} $$ is the highest power common to both).

- **Overall GCF:**  
  Combining the above, the GCF of the entire expression is $$ 8x y^{3} $$.

### 2. Factor Out the GCF
Divide each term by the GCF and factor it out:

$$
48 y^{3} x^{2} - 8 x y^{4} = 8x y^{3} \left( \frac{48 y^{3} x^{2}}{8x y^{3}} - \frac{8 x y^{4}}{8x y^{3}} \right)
$$

Simplify inside the parentheses:

$$
= 8x y^{3} (6x - y)
$$

### 3. Final Factored Form
The completely factored form of the expression is:

$$
\boxed{8x y^{3} \left(6x - y\right)}
$$

This expression cannot be factored further, as $$6x - y$$ is a binomial with no common factors.
The expression $$48 y^{3} x^{2} - 8 x y^{4}$$ can be factored completely as $$8x y^{3} (6x - y)$$.

Recognize the type of expression and use an appropriate method to factor it completely.

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