The expression 6m+15 can be factored into 3(2m+5) using the distributive property. More complex expressions like 44k^5-66k^4 can be factored in much the same way. This article provides a couple of examples and gives you a chance to try it yourself.

Example 1

Both terms share a common factor of 3\goldD{3}, so we factor out the 3\goldD{3} using the distributive property:
6m+15=3(2m+5)\begin{aligned} &6m+15\\\\ =&\goldD{3}(2m+5) \end{aligned}
Want a more in-depth explanation? Check out this video.

Example 2

Factor out the greatest common monomial.
The coefficients are 44,66,44,66, and 7777, and their greatest common factor is 11\blueD{11}.
The variables are k5,k4,k^5, k^4, and k3k^3, and their greatest common factor is k3\blueD{k^3}.
Therefore, the greatest common monomial factor is 11k3\blueD{11k^3}.
Factoring, we get:
44k566k4+77k3=11k3(4k2)+11k3(6k)+11k3(7)=11k3(4k26k+7)\begin{aligned} &44k^5-66k^4+77k^3\\\\ =&\blueD{11k^3}(4k^2)+\blueD{11k^3}(-6k)+\blueD{11k^3}(7)\\\\ =&\blueD{11k^3}(4k^2-6k+7) \end{aligned}
Want another example like this one? Check out this video.


Want more practice? Check out this exercise.