## Expanding (a + 3)(a - 2)

This expression represents the product of two binomials: (a + 3) and (a - 2). To expand it, we can use the **FOIL method**, which stands for **First, Outer, Inner, Last**.

Here's how it works:

**1. First:** Multiply the first terms of each binomial:

- a * a = a²

**2. Outer:** Multiply the outer terms of the binomials:

- a * -2 = -2a

**3. Inner:** Multiply the inner terms of the binomials:

- 3 * a = 3a

**4. Last:** Multiply the last terms of each binomial:

- 3 * -2 = -6

Now, we combine the terms:

a² - 2a + 3a - 6

Finally, simplify by combining like terms:

**a² + a - 6**

Therefore, the expanded form of (a + 3)(a - 2) is **a² + a - 6**.

### Other methods for expanding:

While the FOIL method is commonly used for expanding binomials, you can also use the **distributive property**:

**(a + 3)(a - 2) = a(a - 2) + 3(a - 2)**

Then, distribute each term:

**a(a - 2) + 3(a - 2) = a² - 2a + 3a - 6**

This again leads to the same simplified result: **a² + a - 6**.

### Conclusion

Expanding expressions like (a + 3)(a - 2) is crucial for simplifying algebraic expressions and solving equations. The FOIL method provides a systematic approach, while the distributive property offers an alternative way to achieve the same result.