The distributive property allows you to rewrite expressions by multiplying a sum or difference by a number.
Understanding the Distributive Property
The distributive property states that for any numbers a, b, and c:
a( b + c ) = (a b) + (a c)
This means you can distribute the multiplication across the addition or subtraction within the parentheses.
Rewriting Expressions Using the Distributive Property
Here are some examples of how the distributive property can be used to rewrite expressions:
-
Example 1:
- Original Expression: 3(x + 2)
- Rewritten Expression: 3x + 6
- Explanation: Distribute the 3 to both the x and the 2.
-
Example 2:
- Original Expression: -2(4y - 5)
- Rewritten Expression: -8y + 10
- Explanation: Distribute the -2 to both the 4y and the -5. Remember that a negative times a negative equals a positive.
-
Example 3:
- Original Expression: 5(2a + 3b - 1)
- Rewritten Expression: 10a + 15b - 5
- Explanation: Distribute the 5 to each term inside the parentheses.
Practical Applications
The distributive property is a fundamental concept in algebra and is used extensively in solving equations, simplifying expressions, and working with polynomials.
Conclusion
The distributive property is a powerful tool that helps you rewrite expressions by multiplying a sum or difference by a number. It is a fundamental concept in algebra and is used in various mathematical operations.
