Using the Distributive Property with Variables and Factoring

Miacademy & MiaPrep Learning Channel

This video transitions students from arithmetic to algebraic thinking by demonstrating how to use the Distributive Property when variables are present. It begins by establishing the necessity of the property, explaining that the standard Order of Operations (PEMDAS) cannot be applied to simplify expressions like 3(x + 6) because the value inside the parentheses cannot be computed first. The narrator guides viewers through expanding expressions with single variables, as well as more complex expressions with multiple terms and variables, such as 7(4 - x + y). Key themes include algebraic manipulation, equivalent expressions, and the inverse relationship between multiplication and factoring. The video provides a clear visual demonstration of expanding expressions using the "rainbow" method (drawing arrows to show distribution) and then shifts focus to the reverse operation: factoring out the Greatest Common Factor (GCF). It utilizes prime factorization trees to find the GCF of numbers like 45 and 15, showing students exactly how to rewrite an expanded linear expression in its factored form. This resource is highly valuable for 6th and 7th-grade math classrooms as it bridges concrete arithmetic with abstract algebra. Teachers can use it to introduce equivalent expressions or to scaffold the often-difficult concept of factoring. The step-by-step visual breakdowns, particularly the use of factor trees and color-coded substitution, make it an excellent tool for visual learners and for clarifying common misconceptions, such as failing to distribute to every term or difficulty identifying the GCF.