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Simplifying Using the Distributive Property
Apply the distributive property when a negative factor multiplies a difference. Simplify :
Step 1 — Distribute: Multiply by each term inside the parentheses:
Step 2 — Multiply: Compute each product. For the first term, . For the second term, . The expression becomes:
Step 3 — Simplify: Subtracting a negative is equivalent to adding a positive, so :
The result can also be written as by applying the commutative property of addition to reorder the terms. This example combines three skills in one problem: distributing a negative factor, multiplying signed numbers, and converting the subtraction of a negative into addition. The extra simplification step — recognizing that becomes — is the key detail that distinguishes distributing a negative over a subtraction from distributing over an addition.
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