Factor. $$ 8 s d^{4}-8 s h^{4} $$

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To factor the expression $$ 8s d^{4} - 8s h^{4} $$, follow these steps:

1. **Factor out the Greatest Common Factor (GCF):**
   
   Both terms $$ 8s d^{4} $$ and $$ 8s h^{4} $$ have a common factor of $$ 8s $$.

$$
   8s d^{4} - 8s h^{4} = 8s (d^{4} - h^{4})
   $$

2. **Recognize the Difference of Squares:**

The expression inside the parentheses, $$ d^{4} - h^{4} $$, is a difference of squares because $$ d^{4} = (d^{2})^{2} $$ and $$ h^{4} = (h^{2})^{2} $$.

$$
   d^{4} - h^{4} = (d^{2})^{2} - (h^{2})^{2} = (d^{2} - h^{2})(d^{2} + h^{2})
   $$

3. **Factor the Difference of Squares Further:**

The term $$ d^{2} - h^{2} $$ is also a difference of squares and can be factored:

$$
   d^{2} - h^{2} = (d - h)(d + h)
   $$

4. **Combine All Factors:**

Putting it all together:

$$
   8s (d^{4} - h^{4}) = 8s (d^{2} - h^{2})(d^{2} + h^{2}) = 8s (d - h)(d + h)(d^{2} + h^{2})
   $$

**Final Factored Form:**

$$
8s (d - h)(d + h)(d^{2} + h^{2})
$$

**Answer:**  
After factoring, the expression is 8 s (d – h)(d + h)(d² + h²)
The expression $$ 8s d^{4} - 8s h^{4} $$ factors to $$ 8s (d - h)(d + h)(d^{2} + h^{2}) $$.

Factor. \( 8 s d^{4}-8 s h^{4} \)

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