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Distributive Rule

The most basic type of factoring involves the distributive rule (also know as factoring out a common factor):

ax + ay = a(x + y)

When this rule is applied from left to right, it is called factoring. When the rule is applied from right to left, it is called distributing.
For example, 3h + 3k = 3(h + k), and 5xy + 45x = 5xy + 9 5x = 5x(y + 9). The distributive rule can be generalized to any number of terms. For three terms, it looks like ax + ay + az = a(x + y + z).
For example, .
For another example, .


If x – y = 9, then
A.  –4
B.  –3
C.  0
D.  12
E.  27

   by distributing the negative sign
   by combining the
   by factoring out the common factor 4/3
   since x – y = 9
  The answer is (D).


Column A Column B


 by the rule
 by the distributive property ax + ay = a(x + y)
 by the rule
Hence, the columns are equal, and the answer is (C).

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