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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 x 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, .
 
Example

If x – y = 9, then

  1. –4
  2. –3
  3. 0
  4. 12
  5. 27
Solution

 
by distributing the negative sign
by combining the
by factoring out the common factor 4/3
since x – y = 9
12
 
The answer is (D).
 
 
Example

  1. 29 – 219
  2. 28
  3. 210
  4. 228
Solution

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




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