(a-3).jpeg "(a+5)(a-3)")
Expanding the Expression (a+5)(a-3)
This article will guide you through expanding the expression (a+5)(a-3).
Understanding the Process
Expanding this expression involves multiplying each term in the first set of parentheses by each term in the second set of parentheses. This is often referred to as FOIL (First, Outer, Inner, Last) method:
- First: Multiply the first terms of each binomial: a * a = a²
- Outer: Multiply the outer terms of each binomial: a * -3 = -3a
- Inner: Multiply the inner terms of each binomial: 5 * a = 5a
- Last: Multiply the last terms of each binomial: 5 * -3 = -15
Expanding the Expression
Combining the results of each multiplication:
(a + 5)(a - 3) = a² - 3a + 5a - 15
Simplifying the Result
Finally, combine the like terms:
a² - 3a + 5a - 15 = a² + 2a - 15
Conclusion
Therefore, the expanded and simplified form of (a + 5)(a - 3) is a² + 2a - 15. This process demonstrates the basic principles of algebraic manipulation involving binomial multiplication.