(a-2)-(a-5)(a%2B3).jpeg "(a-1)(a-2)-(a-5)(a+3)")
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.