Final answer:
The expression A (B+C) = AB + AC represents the distributive property in mathematics, allowing one to distribute multiplication across an addition inside parentheses. It's essential for simplifying algebraic expressions and solving equations.
Step-by-step explanation:
When we look at the expression A (B+C) = AB + AC, it illustrates the use of the distributive property. This property allows us to multiply a single term by each term inside a bracket. Essentially, you are distributing the multiplication of A across the addition within the parentheses, resulting in the multiplication of A with both B and C separately and then adding the two products.
The distributive property is different from the commutative property, which states that you can change the order of the numbers in an addition or multiplication equation without changing the result, or the associative property, which allows you to change the grouping of numbers. It is also distinct from the identity property, where adding 0 or multiplying by 1 delivers the original number.
Properties like the distributive property are essential in simplifying algebraic expressions and solving equations. They are basic tools in algebra that help us manipulate and solve expressions and equations effectively.