# 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.

*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 *

*â€“4**â€“3**0**12**2**7*

Solution

by distributing the negative sign | |

by combining the | |

by factoring out the common factor 4/3 | |

since x â€“ y = 9 | |

12 |

Example

- 2
^{9}â€“ 21^{9} - 2
^{8} - 2
^{10} - 2
^{28}

Solution

by the rule | |

by the distributive property ax + ay = a(x + y) | |

by the rule |