27.2: B1.02- Section 1
- Page ID
- 51770
Use the distributive property and other properties to simplify expressions and check your work.
Distributive Property:
For any real numbers a, b, and c: a(b + c) = ab + ac.
For any real numbers a, b, and c: a(b – c) = ab – ac
The fact that two expressions are equal means that they are equal for any values of the variable. So you can check by taking a few values for the variable and making sure that those do make the two sides equal. Usually we don’t use the values 0 or 1 or 2 as the value for the variable and it is best to avoid numbers that already appear in the problem.
Example 1
Simplify .
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Solution: | Partial Check: Use |
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Example 2
Simplify .
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Solution: | Partial Check: Use |
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Example 3
Simplify .
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Solution: | Partial Check: Use |
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Example 4
Simplify .
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Solution: | Partial Check: Use |
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Caution: Checking your work on problems like these is not completely satisfactory, because students who make a mistake in the original solution often make a corresponding mistake in the checking process. So the fact that it checks does not provide complete confidence that the solution is correct. But it’s still a good idea to check because you’ll catch most of your mistakes.
- Mathematics for Modeling. Authored by: Mary Parker and Hunter Ellinger. License: CC BY: Attribution