Final answer:
The statement refers to the distributive property in mathematics, illustrated by the formula A(B + C) = AB + AC. Real-world example: 3(4 + 5) = 12 + 15, yielding the sum 27.
Step-by-step explanation:
The statement in question refers to the distributive property in mathematics. Specifically, it states that the product of a number and a sum is equal to the sum of the individual products of the addends and the number. This can be mathematically represented as A(B + C) = AB + AC. For example, if we take the number 3 and the sum of 4 + 5, applying the distributive property would look like 3(4 + 5) = 3×4 + 3×5 = 12 + 15, which equals 27.
In the context of vector operations, the distributive property is also applicable and allows for expressions such as the dot product to be expanded in terms of scalar components.
The statement A+B=B+A is known as the commutative property of addition, which is a fundamental concept in mathematics. It states that the order of adding two numbers does not affect the result. This property holds true for ordinary numbers as well as for other mathematical operations, such as vectors and probabilities.