Using Properties to Simplify

Algebra 1 · Axiom Academy

EXAMPLE Using Properties to Simplify A step-by-step walkthrough of simplifying an algebraic expression by applying number properties. Simplify the expression 3(2x + 5) - 2(x - 4) by applying the distributive and commutative properties, then combining like terms. Excellent! You've simplified the expression. Here's a recap of the properties we used to get from the initial expression to the final simplified form: Distributive Property: This was our first step to eliminate parentheses. We "distributed" the outside term to each term inside, like 3(2x+5) becoming 6x+15 . Commutative Property: This let us reorder the terms to group variables and constants together, making them easier to manage — for example, putting 6x and -2x next to each other. Combining Like Terms: The final steps performed the addition and subtraction on the grouped terms to reach the simplest form. Result: 3(2x + 5) - 2(x - 4) = 4x + 23 . Applying properties in a deliberate order — clear the parentheses, regroup, then combine — turns a messy expression into a clean one every time.

This is the written version of the interactive lesson above. See the full Algebra 1 course.