## Factoring the Expression (x-3)²(2x+1)³ + (x-3)³(2x+1)²

This article will guide you through factoring the expression (x-3)²(2x+1)³ + (x-3)³(2x+1)².

### Identifying Common Factors

The first step to factoring any expression is to identify common factors. In this case, we can see that both terms share the factors (x-3)² and (2x+1)².

### Factoring Out Common Factors

Now, we can factor out these common factors:

(x-3)²(2x+1)³ + (x-3)³(2x+1)² = **(x-3)²(2x+1)²** [(2x+1) + (x-3)]

### Simplifying the Expression

Simplifying the expression within the brackets, we get:

(x-3)²(2x+1)² [(2x+1) + (x-3)] = **(x-3)²(2x+1)² (3x - 2)**

### Final Factored Form

Therefore, the factored form of the expression (x-3)²(2x+1)³ + (x-3)³(2x+1)² is **(x-3)²(2x+1)² (3x - 2)**.

### Summary

By identifying common factors and factoring them out, we successfully simplified the expression and obtained its factored form. This process can be applied to factor various algebraic expressions.