## Simplifying the Expression (x+1)(x+2)(x+3)(x+4)(x+5)

This expression represents the product of five consecutive factors. While expanding it directly would be quite tedious, we can use a clever trick to simplify it.

### The Trick

The key is to recognize that this expression resembles a pattern found in factorials. Factorials are defined as the product of consecutive integers starting from 1 down to a given number. For example, 5! = 5 * 4 * 3 * 2 * 1.

We can rewrite our expression as:

**(x+5)! / x!**

This is because the product (x+1)(x+2)(x+3)(x+4)(x+5) represents the consecutive integers from (x+1) to (x+5), and dividing by x! eliminates the terms from 1 to x.

### Further Simplification

While this is a simplified form, it can be further expanded for specific values of x. For example, if x = 2, the expression becomes:

7! / 2! = 5040 / 2 = 2520

### Conclusion

Simplifying the expression (x+1)(x+2)(x+3)(x+4)(x+5) can be achieved by recognizing the pattern of factorials and rewriting it as (x+5)! / x!. This form is more concise and easier to work with, especially when dealing with specific values of x.