Algebra I Recipe: The Distributive Property
By G Redden
A. Distributive Property
- Given 3(x + 2), the 3 would be multiplied by the x and the 2, called performing the distributive property and would equal 3x + 6.
- The distributive property is best performed when the operation(s) inside the parentheses can’t be done.
- The distributive property is used to eliminate the parentheses.
- When there is a negative symbol or a negative number in front of the parentheses AND subtraction inside the parentheses, change subtraction to “adding the opposite” before multiplying.
- A negative symbol in front of the parentheses in understood to be a –1, and changes each term inside the parentheses to its opposite.
1.
7(x + 6)
2.
–2(9 - x)
3.
(3x - 4)3
4.
x(8 + 4x)
5.
–x(5x + 6)
6.
-4(6x - 5)
7.
-(-x + 2)
8.
-(3x - 7)
B. Combining Like Terms and Simplifying Algebraic Expressions* Given –8x, -8 is the coefficient.
* Terms are separated by addition and subtraction.
* Like terms must have the same exact variable(s) with the same exact exponents;
that is, the only difference is the coefficients.
- Change subtraction to “adding the opposite” where necessary.
- Do the distributive property.
- Combine like terms by combining their coefficients. Exponents DO NOT change.
- In the answer, terms go in descending order by powers or in alphabetical order.
9.
3x - 4 + 5x
10.
5y + 6x + 7y + 2x
11.
3(2x - 8) + 20
12.
14 - (3x + 12)
13.
-x3 + 2x(x - x2)
