## Expanding the Expression (a-1)(2a+5)

This article will explore the process of expanding the expression **(a-1)(2a+5)**, which is a product of two binomials. This expansion is a fundamental concept in algebra, often encountered in solving equations, simplifying expressions, and working with quadratic functions.

### The FOIL Method

The most common method for expanding such expressions is the **FOIL** method. FOIL stands for:

**F**irst: Multiply the first terms of each binomial.**O**uter: Multiply the outer terms of the binomials.**I**nner: Multiply the inner terms of the binomials.**L**ast: Multiply the last terms of each binomial.

Let's apply FOIL to our expression:

**F:** (a) * (2a) = **2a²**
**O:** (a) * (5) = **5a**
**I:** (-1) * (2a) = **-2a**
**L:** (-1) * (5) = **-5**

Now, we combine the terms:

2a² + 5a - 2a - 5

Finally, we simplify by combining like terms:

**2a² + 3a - 5**

### Conclusion

By using the FOIL method, we have successfully expanded the expression **(a-1)(2a+5)** into its simplified form, **2a² + 3a - 5**. This process demonstrates a fundamental algebraic technique with applications in various mathematical contexts.