But it explains why you are arbitrarily dividing 6 out and often factoring is taught on an expression first. So it keeps the equivalent expressions from step to step.

Just to be clear, I dislike "slide & divide". I start teaching factoring from multiplication, then area model, then grouping and then open it up to creative ideas like what you have shown here.

I use these ideas with my ALG1 kiddos to help build their number fluency and flexibility. They can easily graph the big picture ideas of multiply by one and the advantage of splitting that up into the two processes of multiply now and divide later.

I write line 1 as multiplying by 6/6, therefore not changing the value of the polynomial. I leave 1/6 outside brackets while doing the steps as shown then the second to the last step makes sense.