Equivalent expressions represent the same quantity and produce the same value for every allowed value of the variable, even when their forms look different. This understanding includes using the commutative, associative, and distributive properties, combining like terms, and interpreting expressions with whole-number coefficients, variables, and parentheses; it excludes advanced polynomial identities and expressions involving more complex number systems. Recognizing equivalence supports simplifying, evaluating, and transforming expressions in later algebra.
Equivalent expressions may look different but have the same value for every allowed value of the variable.
To identify equivalent expressions, rewrite one expression using properties and combine like terms.
Example: Are and equivalent?
Distribute the to each term inside the parentheses:
Combine like terms. The terms and both have , so add their coefficients:
The expression becomes:
So, and are equivalent expressions.
You can check by choosing a value, such as :
and
Both expressions give the same value.
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