Distributive property

Learning Objectives Define the distributive property and explain its purpose. Apply the distributive property to numerical expressions involving multiplication over addition. Apply the distributive property to numerical expressions involving multiplication over subtraction. Use the distributive property to simplify algebraic expressions with one variable. Identify equivalent expressions created using the distributive property. Use the distributive property as a mental math strategy for multiplication. Ever wonder how to multiply a number by a sum or difference quickly in your head? 🤔 It's easier than you think with a special math trick! In this lesson, you'll discover the distributive property, a powerful tool that helps us break down multiplication problems into...

TermDefinitionExample Distributive PropertyA property that states multiplying a number by a sum or difference is the same as multiplying that number by each part of the sum or difference and then adding or subtracting the products.3 × (4 + 2) is the same as (3 × 4) + (3 × 2). ExpressionA mathematical phrase that can contain numbers, variables, and operation symbols, but no equal sign.5 + 3x or 7(y - 2) TermA single number, a single variable, or numbers and variables multiplied together, separated by addition or subtraction signs in an expression.In the expression 2x + 5, '2x' is a term and '5' is a term. FactorA number or expression that is multiplied by another number or expression to get a product.In 4(x + 3), '4' is a factor and '(x + 3)' is a fa...

Distributive Property over Addition $$a(b + c) = ab + ac$$ To multiply a number 'a' by a sum (b + c), you multiply 'a' by 'b' and 'a' by 'c', then add the results. Distributive Property over Subtraction $$a(b - c) = ab - ac$$ To multiply a number 'a' by a difference (b - c), you multiply 'a' by 'b' and 'a' by 'c', then subtract the second result from the first.