Factor using the distributive property

Learning Objectives Define factors, common factors, and the greatest common factor (GCF). Identify the greatest common factor (GCF) of two or more numbers. Explain the relationship between the distributive property and factoring. Factor numerical expressions using the distributive property. Factor simple algebraic expressions using the distributive property. Check their factored expressions by applying the distributive property. Have you ever needed to share a group of items equally, or combine groups in a smart way? 🤔 Understanding how to 'factor' can make these tasks much easier! In this lesson, you'll learn how to take an expression and rewrite it as a product of factors, using a special trick called the distributive property in reverse. This skill helps...

TermDefinitionExample FactorA factor is a number that divides another number evenly, without leaving a remainder. When two or more numbers are multiplied, each number is a factor of the product.The factors of 12 are 1, 2, 3, 4, 6, and 12. (Because 1x12=12, 2x6=12, 3x4=12) Common FactorA common factor is a factor that two or more numbers share.For 12 and 18, the factors of 12 are {1, 2, 3, 4, 6, 12} and the factors of 18 are {1, 2, 3, 6, 9, 18}. The common factors are {1, 2, 3, 6}. Greatest Common Factor (GCF)The greatest common factor (GCF) is the largest number that is a factor of two or more numbers.For 12 and 18, the common factors are {1, 2, 3, 6}. The greatest common factor (GCF) is 6. Distributive PropertyThe distributive property states that multiplying a number by a sum (or differ...

The Distributive Property $a(b+c) = ab + ac$ This rule shows how to multiply a number by a sum. You multiply 'a' by 'b' and 'a' by 'c', then add the results. Factoring using the Distributive Property (Reverse Distributive Property) $ab + ac = a(b+c)$ This rule shows how to factor an expression. If two terms share a common factor 'a', you can 'pull out' 'a' and write the remaining parts 'b' and 'c' inside parentheses, connected by the original operation. Steps to Factor an Expression 1. Find the GCF of all terms in the expression. 2. Divide each term by the GCF. 3. Write the GCF outside parentheses, and the results from step 2 inside the parentheses, connected by the original opera...