## Simplifying the Expression: (a-1)(a-2) - (a-5)(a+3)

This article will walk through the process of simplifying the expression: **(a-1)(a-2) - (a-5)(a+3)**.

### Expanding the Expressions

To begin, we need to expand the products using the distributive property (or FOIL method).

**(a-1)(a-2)**= a(a-2) - 1(a-2) = a² - 2a - a + 2 =**a² - 3a + 2****(a-5)(a+3)**= a(a+3) - 5(a+3) = a² + 3a - 5a - 15 =**a² - 2a - 15**

### Combining the Expanded Expressions

Now that we've expanded the products, we can substitute them back into the original expression:

(a-1)(a-2) - (a-5)(a+3) = (a² - 3a + 2) - (a² - 2a - 15)

To simplify further, we need to distribute the negative sign in front of the second set of parentheses:

(a² - 3a + 2) - (a² - 2a - 15) = a² - 3a + 2 - a² + 2a + 15

### Combining Like Terms

Finally, we combine the like terms:

a² - 3a + 2 - a² + 2a + 15 = **-a + 17**

### Conclusion

Therefore, the simplified form of the expression (a-1)(a-2) - (a-5)(a+3) is **-a + 17**.