Distributiivsusomadus

Distributiivsusomadus, often translated as the distributive property, is a fundamental concept in algebra and arithmetic. It describes a relationship between multiplication and addition, or more generally, between two binary operations. The property states that when a number or expression is multiplied by a sum, it is equivalent to multiplying the number or expression by each term in the sum individually and then adding the results. Mathematically, for numbers a, b, and c, the distributive property is expressed as a(b + c) = ab + ac. This holds true for real numbers, complex numbers, and many other algebraic structures. The order of multiplication does not matter, so (b + c)a = ba + ca is also a valid representation of the distributive property. This property is crucial for simplifying algebraic expressions, solving equations, and performing various mathematical manipulations. It allows us to expand or factor expressions, making them easier to understand or work with. For example, 3(x + 2) can be expanded to 3x + 6 using the distributive property. Conversely, 3x + 6 can be factored to 3(x + 2). Understanding and applying the distributive property is a cornerstone of mathematical fluency.