The expression you provided is \(36 - h^6\). This is a difference of terms where one term is a constant (\(36\)) and the other is a sixth power of \(h\) (\(h^6\)).

### Simplification and Factorization

1. **Simplification:** The expression \(36 - h^6\) is already in its simplest form.

2. **Difference of Squares:**
   The expression can be factored using the difference of squares method, although this is technically a difference of powers, we can rewrite it to apply difference of squares:

   \[
   36 - h^6 = (6^2) - (h^3)^2
   \]

   \[
   = (6 - h^3)(6 + h^3)
   \]

   Each of these factors can potentially be further factored, particularly if you want to break down the difference of cubes as follows:

3. **Difference of Cubes:**

   The expression can also be rewritten as a difference of cubes if desired:

   - Factor the difference of cubes from \( (6 - h^3) \):

   \[
   6 - h^3 = (a^3 - b^3) = (a-b)(a^2 + ab + b^2)
   \]

   where \( a = \sqrt[3]{6} \) and \( b = h \). However, using actual cube roots is impractical in basic simplification without knowing the exact numeric value of \(\sqrt[3]{6}\).

   - Apply to \( (6 + h^3) \) similarly for sums of cubes, though this leads to complex numbers if taken directly.

### Conclusion

Since the question does not specify what operation to apply beyond factorization, the expression \(36 - h^6\) as written in the simplest terms with factoring as \((6-h^3)(6+h^3)\) may suffice unless further context for solving is needed.

If you have any specific operations or a particular direction you’d like to take with this expression, please let me know!

Would you like more details, or do you have any questions? 

Here are some related questions to explore further:

1. What are the steps to factor a difference of cubes?
2. How can the expression \(36 - h^6\) be rewritten using radicals?
3. How do you factor higher-degree polynomials?
4. What are the applications of the difference of squares in algebra?
5. How is a sum of cubes different from a difference of cubes in factorization?
6. What techniques are used to solve polynomial equations?
7. How can you graph the function \(y = 36 - h^6\)?
8. What are some common mistakes to avoid when factoring polynomials?

**Tip:** Always check if expressions can be factored using common techniques such as difference of squares or cubes, as this can simplify calculations and solutions.

Learn how to factorize the expression 36 - h^6 using difference of squares and cubes methods. This problem covers key algebraic concepts, including polynomial factorization techniques. Suitable for students studying algebra in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation