Distributive Property
The distributive property is a fundamental property in mathematics that helps simplify expressions by breaking them down into smaller parts. It states that when multiplying a sum by a number, you can distribute the number to each term within the sum. This property is often used in algebra to manipulate and simplify equations.

Explanation
- The distributive property is expressed as: a(b + c) = ab + ac, where a, b, and c are any real numbers.
- This property allows us to distribute the number outside the parentheses to each term inside the parentheses.
- For example, if we have 2(3 + 4), we can apply the distributive property to get: 2(3) + 2(4) = 6 + 8 = 14.
- Similarly, the distributive property can be used in reverse to factor out a common term from each expression.
- For instance, in the expression 5x + 10y, we can factor out the common factor 5 to get: 5(x + 2y).

Importance
- The distributive property is essential in simplifying algebraic expressions and solving equations.
- It allows for easier manipulation of terms and helps in performing arithmetic operations efficiently.
- Understanding and applying the distributive property can make complex problems more manageable and lead to accurate solutions.
In conclusion, the distributive property is a powerful tool in mathematics that aids in simplifying expressions and solving equations. Mastering this property is crucial for success in algebra and beyond.