66(y root -5y cube -24 y square ÷6y(y-8 divide the following by the method of factorsisation 

It seems like you're asking to factorize and divide the following expression using factorization techniques:

\[ 66y \left( \sqrt{y} - 5y^3 - \frac{24y^2}{6y} \right) \div 6y(y - 8) \]

Let's break this down step by step.

### 1. Simplify the Inside Expression
First, let's simplify the expression inside the parentheses:

\[ \sqrt{y} - 5y^3 - \frac{24y^2}{6y} \]

1. Simplify the fraction:
   \[ \frac{24y^2}{6y} = 4y \]

So the expression becomes:

\[ \sqrt{y} - 5y^3 - 4y \]

### 2. Factorize the Numerator
The expression becomes:

\[ 66y(\sqrt{y} - 5y^3 - 4y) \]

Let's check for common factors or factorize the expression inside the parentheses. 

Unfortunately, the expression \(\sqrt{y} - 5y^3 - 4y\) doesn't easily factorize in a simple way, so let's focus on the division.

### 3. Simplify the Division
Now, let's simplify the overall expression:

\[ \frac{66y(\sqrt{y} - 5y^3 - 4y)}{6y(y - 8)} \]

1. Cancel the common factor \(6y\) from the numerator and denominator:
   \[ \frac{66y}{6y} = 11 \]

So the expression simplifies to:

\[ 11(\sqrt{y} - 5y^3 - 4y) \div (y - 8) \]

### 4. Final Expression
This simplifies the expression as much as possible. So, the result is:

\[ 11 \left( \frac{\sqrt{y} - 5y^3 - 4y}{y - 8} \right) \]

Further factorization depends on the specific values of \(y\) or context, but generally, this is the most simplified form.

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**Would you like more details on any step or a different approach?**

### Related Questions:
1. How do you factorize quadratic expressions?
2. What is the process of simplifying algebraic fractions?
3. How do you factor out common terms in algebraic expressions?
4. What are the methods for simplifying expressions involving roots?
5. How can the division of polynomials be performed?
6. What are the techniques for solving expressions with radicals?
7. What are the different methods of factorization in algebra?
8. How do you simplify expressions involving cube and square terms?

**Tip:** Always check if an expression can be factored or simplified before performing operations like division. This can often simplify the calculation and reveal patterns.

Learn how to factorize and divide complex polynomials involving radical, exponential, and variable terms. This problem covers key algebraic concepts including factorization, polynomial division, and simplification of expressions. Suitable for high school students studying advanced algebra.

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