Equivalent expressions represent the same value for every permissible value of their variables, even when their terms or structure look different. Using commutative and associative properties to reorder or regroup, the distributive property to expand or factor, and combining like terms such as , learners rewrite expressions while preserving their meaning; unlike terms cannot be combined. This understanding supports simplifying expressions and solving equations later.
Equivalent expressions may look different but have the same value for every allowed value of the variable. To rewrite an expression, use properties that preserve its value.
Example: Rewrite and simplify
Step 1: Use the distributive property.
Multiply by each term inside the parentheses:
Step 2: Combine like terms.
The terms and are like terms because both have :
The number is not like an -term, so it stays separate.
Step 3: Write the equivalent expression.
So, the simplified equivalent expression is:
Each step keeps the expression’s value the same; only its form changes.
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