Final answer:
The property described, which allows for the distribution of multiplication across addition within parentheses, resulting in equivalent expressions like A(B+C) = AB + AC, is known as the Distributive Property.
Step-by-step explanation:
The mathematical property being described is the Distributive Property. This property is evident when an operation is carried out across an addition within parentheses, such as in the expression A(B+C) which equals AB + AC. The property signifies that a factor outside the parentheses can be distributed, or multiplied, to each addend within the parentheses to produce an equivalent expression. The Distributive Property is vital in various areas of algebra, including working with vectors in physics, as it allows for the multiplication of a scalar with a sum of vectors and the break down of complex expressions into simpler ones.