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Simplifying Using the Distributive Property
Apply the distributive property when the outside factor is a negative number. Simplify :
Step 1 — Distribute: Multiply by each term inside the parentheses:
Step 2 — Multiply: Compute each product. For the first term, (different signs produce a negative coefficient). For the second term, :
The simplified result is . When the factor outside the parentheses is negative, every product picks up a sign change compared to distributing a positive factor. A useful check is to verify that each term in the result has the opposite sign from what it would have if the outside factor were positive — here, would give , and flipping both signs gives .
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