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Simplifying Using the Distributive Property
Use the distributive property to simplify , an expression whose terms inside the parentheses ( and ) are unlike and cannot be added:
Step 1 — Distribute: Multiply the outside factor by each term inside the parentheses separately:
Step 2 — Multiply: Compute each product: and :
The simplified result is . This is a fundamental application of the distributive property in algebra: when a number multiplies a sum that contains a variable term, each term inside the parentheses is multiplied by that number individually. Unlike , where the associative property suffices because both factors are multiplied together, here two separate products must be formed and then combined with addition.
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