Final answer:
The property a(b + c) = ab + ac is known as the distributive property. It is fundamental in algebra for multiplying a term across the terms within parentheses and simplifying expressions.
Step-by-step explanation:
The property represented by the equation a(b + c) = ab + ac is known as the distributive property. This property allows us to multiply a single term by each term inside a parenthesis. For example, if we have 3(1 + 2), using the distributive property, we would do 3 × 1 + 3 × 2, which simplifies to 3 + 6, giving us a result of 9.
This distributive law is very useful in algebra for simplifying expressions and solving equations. Additionally, it is applied in various branches of mathematics and is essential in more advanced topics including vector calculations and polynomial multiplication. In chemistry, this property is analogous to how stoichiometric coefficients are used when writing rate laws for chemical reactions, where the rate can be expressed using the concentrations of the reactants multiplied by their respective coefficients, as seen in the reaction rate expression rate = k[A][B].