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Algebra I Recipe: The Distributive Property
A. Distributive Property
  1. 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.
  2. The distributive property is best performed when the operation(s) inside the parentheses can’t be done.
  3. The distributive property is used to eliminate the parentheses.
  4. 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.
  5. A negative symbol in front of the parentheses in understood to be a –1, and changes each term inside the parentheses to its opposite.
7(x + 6)
–2(9 - x)
(3x - 4)3
x(8 + 4x)
–x(5x + 6)
-4(6x - 5)
-(-x + 2)
-(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.
  1. Change subtraction to “adding the opposite” where necessary.
  2. Do the distributive property.
  3. Combine like terms by combining their coefficients. Exponents DO NOT change.
  4. In the answer, terms go in descending order by powers or in alphabetical order.
3x - 4 + 5x
5y + 6x + 7y + 2x
3(2x - 8) + 20
14 - (3x + 12)
-x3 + 2x(x - x2)

G Redden

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