The distributive property in math allows you to simplify expressions by distributing a factor to each term within parentheses. In simpler terms, it means you can multiply a number outside the parentheses by each number inside the parentheses and then add the results. [br][br]~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[br][br][b]The Concept:[br][br][/b]When you have a number (or variable) multiplying a sum or difference within parentheses, the distributive property lets you "distribute" that number to each term inside the parentheses.[br][br]This means you multiply the number outside by each term inside separately, then add (or subtract) the results. [br][br]~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[br][br][b]The Formula:[br][br][/b]The distributive property is often written as: a * (b + c) = (a * b) + (a * c) [br][br]It also applies to subtraction: a * (b - c) = (a * b) - (a * c) [br][br]Where 'a', 'b', and 'c' can be numbers or variables. [br][br]~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[br][br][b]Example:[br][br][/b]Let's say you have the expression 3 * (4 + 2).[br][br]Using the distributive property:[br][br]3 * (4 + 2) = (3 * 4) + (3 * 2)[br][br]= 12 + 6[br][br]= 18[br][br]This is the same as first adding inside the parentheses (4 + 2 = 6) and then multiplying (3 * 6 = 18). [br][b][br][/b]~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[br][br][b]Why is it useful?[br][br][/b]The distributive property helps simplify expressions, especially when terms inside parentheses cannot be combined (e.g., when they involve variables).[br][br]It's a fundamental concept used in algebra to solve equations and simplify expressions. [br][b][br][/b]~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[b][br][/b]