# 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, 3
For example, .
For another example, .

*h*+ 3*k*= 3(*h*+*k*), and 5*xy*+ 45*x*= 5*xy*+ 9 â€” 5*x*= 5*x*(*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*).

Example

*If x â€“ y = 9, then*

A. â€“4

B. â€“3

C. 0

D. 12

E. 27

A. â€“4

B. â€“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 â€“ y = 9

12
The answer is (D).

by combining the

by factoring out the common factor 4/3

since x â€“ y = 9

12

Example

Column A | Column B |

2^{8} |

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).