The most common type of distribution is the distributive property of multiplication over addition. This property states that when multiplying a number or expression by a sum or difference, you can distribute the multiplication to each term within the sum or difference separately.
For example:
a(b + c) = ab + ac
Here, the number 'a' is distributed to both 'b' and 'c' within the parentheses.
The distributive property also holds true for subtraction:
a(b - c) = ab - ac
In this case, the number 'a' is distributed to both 'b' and 'c', with 'c' being subtracted.
The distributive property can be used to simplify expressions and perform calculations more efficiently. It applies not only to numbers but also to algebraic expressions containing variables. Here's another example:
3(2x + 5) = 6x + 15
By distributing the '3' to the terms inside the parentheses (2x and 5), we get the simplified expression.
Distribution plays a crucial role in various areas of mathematics, from simplifying algebraic expressions to solving equations, expanding polynomials, and performing algebraic manipulations. It is a fundamental concept that facilitates solving complex mathematical problems.