Distributive property

Learning Objectives Identify the distributive property in mathematical expressions. Apply the distributive property to simplify expressions involving addition and subtraction. Use the distributive property to multiply a number by a sum or difference mentally. Simplify algebraic expressions by distributing a numerical coefficient to terms within parentheses. Recognize and correct common errors when applying the distributive property. Factor out a common numerical factor from an expression using the reverse distributive property. Ever wonder how to share a pizza equally among friends, even when some want different toppings? 🍕 The distributive property helps us share numbers and variables fairly! In this lesson, you'll learn about the distributive property, a powerful to...

TermDefinitionExample Distributive PropertyA property that allows you to multiply a sum or difference by multiplying each number in the sum or difference by the number outside the parentheses.3(x+2) becomes 3x + 6. ExpressionA mathematical phrase that can contain numbers, variables, and operation symbols, but does not have an equality sign.5x + 7 or 2(y-3). TermA single number, a variable, or a product/quotient of numbers and variables in an expression. Terms are separated by addition or subtraction signs.In the expression 3x + 6, '3x' is a term and '6' is a term. CoefficientThe numerical factor of a term that contains a variable.In the term 5x, 5 is the coefficient. In the term y, the coefficient is 1. VariableA symbol, usually a letter, that represents an unknown num...

Distributive Property over Addition $a(b+c) = ab + ac$ To multiply a number by a sum, multiply the number by each term inside the parentheses and then add the products. Distributive Property over Subtraction $a(b-c) = ab - ac$ To multiply a number by a difference, multiply the number by each term inside the parentheses and then subtract the products. Reverse Distributive Property (Factoring) $ab + ac = a(b+c)$ and $ab - ac = a(b-c)$ If two terms share a common factor, you can 'factor out' that common factor, writing the expression as a product of the common factor and the sum/difference of the remaining terms.