The Distributive Property Help
The Distributive Property
An important property that is often used in algebra is called the distributive property :
For any numbers a, b, and c, a(b + c) = ab + ac .
The distributive property states that when a sum of two numbers or expressions in parentheses is multiplied by a number outside the parentheses, the same result will occur if you multiply each number or expression inside the parentheses by the number outside the parentheses.
Multiply 5(2x + 3y).
Multiply 8(x + 3y).
The distributive property also works for subtraction.
Multiply 9(2x – 4y).
The distributive property works for the sum or difference of three or more expressions in parentheses.
Multiply 3(6a + 2b – 7c).
When a negative number is multiplied, make sure to change the signs of the terms inside the parentheses when multiplying.
Multiply –2(6p – 7q – 3r).
Math Note: The distributive property is called the distributive property for multiplication over addition.
Multiply each of the following:
1. 6(3x + 8y)
2. 2(b + 4)
3. 4(7a – 2b + 3c)
4. –3(2p – 5q + 3r)
5. –5(6x – 7y + z)
1. 18x + 48y
2. 2b + 8
3. 28a – 8b + 12c
4. –6p + 15q – 9r
5. –30x + 35y – 5z
Practice problems for this concept can be found at: Expressions And Equations Practice Test.
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