- The Distributive Property of Multiplication is a fundamental property in mathematics that allows us to simplify expressions and perform calculations efficiently. It states that when we multiply a number by a sum or difference of numbers, we can distribute the multiplication to each term inside the parentheses.

Definition:
The distributive property of multiplication over addition states that for any three real numbers a, b, and c, the following equation holds true:
a x (b + c) = a x b + a x c
- This property is also known as the distributive property of multiplication over subtraction, which states that for any three real numbers a, b, and c, the following equation holds true:
a x (b - c) = a x b - a x c

Example:
Let's consider an example to understand the distributive property better:
2 x (3 + 4) = 2 x 3 + 2 x 4
=> 2 x 7 = 6 + 8
=> 14 = 14
- In this example, we distribute the multiplication of 2 to both 3 and 4 inside the parentheses, simplifying the expression on both sides of the equation.

Applications:
- The distributive property is widely used in algebraic expressions, equations, and arithmetic calculations to simplify complex expressions and solve problems efficiently.
- It is a fundamental concept in mathematics and is essential for understanding higher-level mathematical concepts.
- By understanding and applying the distributive property of multiplication, students can simplify expressions, solve equations, and manipulate numbers more effectively in various mathematical contexts.