distributiver

The distributive property is a fundamental concept in mathematics, particularly in algebra and arithmetic. It refers to the ability to distribute a term across addition or subtraction within parentheses. This property is crucial for simplifying expressions and solving equations.

In arithmetic, the distributive property states that for any numbers a, b, and c, the following equation holds true:

a * (b + c) = (a * b) + (a * c)

This means that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. For example, 3 * (4 + 2) equals (3 * 4) + (3 * 2), which simplifies to 12 + 6, or 18.

In algebra, the distributive property is used to expand expressions and factor polynomials. For example, expanding the expression 2(x + 3) using the distributive property results in 2x + 6. Conversely, factoring the expression 4x + 12 using the distributive property results in 4(x + 3).

The distributive property is a key tool in mathematical problem-solving and is essential for understanding more advanced concepts in algebra and calculus. It is widely applicable in various fields, including physics, engineering, and computer science.