2(x+3) Expanded: Understanding the Distributive Property
What is the Distributive Property?
In algebra, the distributive property is a fundamental concept that helps us expand and simplify algebraic expressions. It states that multiplication distributes over addition, meaning that we can multiply a single value to multiple terms inside a parenthesis. The formula for the distributive property is:
a(b + c) = ab + ac
Expanding 2(x+3)
Now, let's apply the distributive property to expand the expression 2(x+3). To do this, we'll multiply the 2 outside the parenthesis to both the x and the 3 inside the parenthesis:
2(x+3) = 2x + 2(3)
= 2x + 6
Therefore, the expanded form of 2(x+3) is 2x + 6.
Why is Expanding Important?
Expanding algebraic expressions is an essential step in solving equations and simplifying complex expressions. By applying the distributive property, we can break down expressions into simpler terms, making it easier to solve problems and understand the underlying math.
Real-World Applications
The distributive property has many real-world applications, such as:
- Finance: Calculating interest rates and investments
- Physics: Modeling motion and force
- Computer Science: Optimizing algorithms and data structures
Conclusion
In this article, we've explored the distributive property and how it's used to expand algebraic expressions. By applying this property, we can simplify complex expressions and solve problems more efficiently. Remember, 2(x+3) expands to 2x + 6!
