HELP! Factor u^2 - 3uv - 6uw + 18vw Completely

[loseratmath]

In New York, we take Math A, Math B, etc. So now I'm in a transition class to Math B (Algebra II+III) So I *think* this is where it goes.

I've been baffled by this problem since 8:00pm and I completely forgot how to do this. Any help is greatly appreciated! I'm not entirely sure as to how to factor it.

u^2 - 3uv - 6uw + 18vw

I tried

3(-uv - 2uw + 6vw) u^2

I get lost from then on..

 

[Denis]

(u - 3v)(u - 6w)

I don't have anything "magic" for you; I used the quadratic;
someone will probably have an ingenious manipulation...

> u^2 - 3uv - 6uw + 18vw
> I tried
> 3(-uv - 2uw + 6vw) u^2
Huh? That should be 3(-uv - 2uw + 6vw) + u^2 : CAREFUL :shock:

 

[loseratmath]

(u - 3v)(u - 6w)

I don't have anything "magic" for you; I used the quadratic;
someone will probably have an ingenious manipulation...

> u^2 - 3uv - 6uw + 18vw
> I tried
> 3(-uv - 2uw + 6vw) u^2
Huh? That should be 3(-uv - 2uw + 6vw) + u^2 : CAREFUL :shock:

I feel like such an idiot, I kept thinking there was this way where I had to use like terms and everything, and y'know stressing myself out. Thank you soo much!

 

[Deleted member 4993]

In New York, we take Math A, Math B, etc. So now I'm in a transition class to Math B (Algebra II+III) So I *think* this is where it goes.

I've been baffled by this problem since 8:00pm and I completely forgot how to do this. Any help is greatly appreciated! I'm not entirely sure as to how to factor it.

u^2 - 3uv - 6uw + 18vw

= u * (u - 3v) - 6w * (u - 3v) ................just by observation.

= (u - 3v) * (u - 6w)

I tried

3(-uv - 2uw + 6vw) u^2

I get lost from then on..