## Factoring and Simplifying Algebraic Expressions

This article will explore the process of factoring and simplifying the following algebraic expression:

**(9x^4y^3 - 15x^3y^4) 3x^2y^2 + 5xy^2**

### Step 1: Factor out the Greatest Common Factor (GCF)

First, we identify the greatest common factor (GCF) of the expression within the parentheses. Both terms have a common factor of **3x^3y^3**. Factoring this out, we get:

**(9x^4y^3 - 15x^3y^4) = 3x^3y^3(3x - 5y)**

### Step 2: Substitute the Factored Expression

Now we can substitute this factored expression back into the original equation:

**3x^3y^3(3x - 5y) 3x^2y^2 + 5xy^2**

### Step 3: Simplify the Expression

We can simplify the expression by multiplying the terms:

**9x^5y^5(3x - 5y) + 5xy^2**

### Step 4: Expand the Expression

To get the final simplified form, we expand the first term:

**27x^6y^5 - 45x^5y^6 + 5xy^2**

### Conclusion

Therefore, the factored and simplified form of the expression **(9x^4y^3 - 15x^3y^4) 3x^2y^2 + 5xy^2** is **27x^6y^5 - 45x^5y^6 + 5xy^2**.

This process demonstrates the importance of factoring and simplifying algebraic expressions to obtain a more concise and understandable representation.