Distribution Property of Integers
The distribution property of integers is a fundamental concept in mathematics that describes how multiplication distributes over addition and subtraction. This property allows us to simplify expressions involving integers and is essential for performing arithmetic operations efficiently.

Definition
The distribution property states that for any integers a, b, and c:
a * (b + c) = a * b + a * c
and
a * (b - c) = a * b - a * c

Example
For example, let's consider the integers 2, 3, and 4:
2 * (3 + 4) = 2 * 3 + 2 * 4
2 * 7 = 6 + 8
14 = 14
Similarly,
2 * (3 - 4) = 2 * 3 - 2 * 4
2 * (-1) = 6 - 8
-2 = -2

Importance
The distribution property is crucial in simplifying algebraic expressions, solving equations, and manipulating integers in various mathematical contexts. It allows us to break down complex calculations into simpler steps and ensures that the rules of arithmetic hold true for integers.

Applications
The distribution property is extensively used in algebra, number theory, and various branches of mathematics. It forms the basis for understanding more advanced concepts such as polynomial multiplication, factorization, and linear equations. Mastery of the distribution property is essential for building a strong foundation in mathematics.