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The given expression to be simplified by factorization is:

\[
\frac{36(y^4 - 5y^3 - 24y^2)}{9y(y - 8)}
\]

### Step 1: Factor the numerator
We start by factoring the numerator:

\[
36(y^4 - 5y^3 - 24y^2)
\]

We can factor out \(36y^2\) from the expression:

\[
36y^2(y^2 - 5y - 24)
\]

Now we need to factor the quadratic expression \(y^2 - 5y - 24\).

To factor \(y^2 - 5y - 24\), we look for two numbers whose product is \(-24\) and whose sum is \(-5\). These numbers are \(-8\) and \(3\). So, we can factor the quadratic as:

\[
y^2 - 5y - 24 = (y - 8)(y + 3)
\]

Thus, the numerator becomes:

\[
36y^2(y - 8)(y + 3)
\]

### Step 2: Simplify the denominator
The denominator is:

\[
9y(y - 8)
\]

### Step 3: Simplify the entire expression
Now we can simplify the full expression:

\[
\frac{36y^2(y - 8)(y + 3)}{9y(y - 8)}
\]

We can cancel out the common factors of \(9y\) and \((y - 8)\):

\[
\frac{36y^2(y - 8)(y + 3)}{9y(y - 8)} = \frac{36y^2(y + 3)}{9y} = 4y(y + 3)
\]

### Final Answer:
The simplified expression is:

\[
4y(y + 3)
\]

Would you like more details on any part of the solution or further clarification?

Here are some related questions for practice:
1. How do you factor a quadratic expression?
2. What is the difference between common factor and grouping methods in factorization?
3. How do you identify common factors in polynomial expressions?
4. How can you apply factorization to simplify fractions?
5. What are the steps to cancel common factors in algebraic expressions?

**Tip:** Always check if you can factor out a greatest common factor (GCF) before proceeding with more complex factorization techniques.

Divide the following by the method of factorization: 36(y^4 - 5y^3 - 24y^2) ÷ 9y(y - 8)

Learn how to factorize and simplify the expression 36(y^4 - 5y^3 - 24y^2) ÷ 9y(y - 8) using the method of factorization. This step-by-step solution covers algebraic factorization and polynomial division concepts for students in Grade 9-10.

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