Raziaar
I Hate Custom Titles
- Joined
- Sep 13, 2003
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Okay so I'm sitting here just reviewing all my math, and I've been looking at multiplying polynomials.
Simple problems using the foil method, for example:
(3q - 8r)^2
Doing it the standard FOIL way is pretty easy... but I was thinking in my head of a shortcut, and this might be a common one, I don't know. I do believe that it doesn't work when the said polynomial is cubed though or any greater factor.
But what I was doing is taking the first polynomial, and cubing it. Thus 3q becomes
9q^2
Then I take the second polynomial and multiply the coefficient by the power of two, so I have -16r. I then take that, and multiply it with the first polynomial which gives me
-48qr
Lastly, I take the second polynomial again, and square it, so that -8r becomes +64r^2
And simply stringing them together I have:
9q^2 - 48qr + 64r^2
And that's the answer... and it's worked on quite a few of them like this(polynomials being squared), but not being cubed.
I was just wondering, can somebody help me to determine if this is a common shortcut, or if it even holds true all of the time? I'm worried if I try to use it for problems like that, it may end up failing some of the time, even though it succeeds some of the time.
Oh well... just a simple gradeschool math thread from me... reviewing all my math up to algebra 2 so I can take this stupid GED test. I'm just hoping I can count on this shortcut to be reliable under this certain scenario if I'm presented with any such problems, since I can do it quickly in my head, much faster than doing the FOIL method.
EDIT: I know this is a pretty pointless dumb thread, and the shortcut has only an incredibly limited use, but I dunno... figured I'd make it anyways. And yes, I know... this thread makes me both look and feel stupid.
Simple problems using the foil method, for example:
(3q - 8r)^2
Doing it the standard FOIL way is pretty easy... but I was thinking in my head of a shortcut, and this might be a common one, I don't know. I do believe that it doesn't work when the said polynomial is cubed though or any greater factor.
But what I was doing is taking the first polynomial, and cubing it. Thus 3q becomes
9q^2
Then I take the second polynomial and multiply the coefficient by the power of two, so I have -16r. I then take that, and multiply it with the first polynomial which gives me
-48qr
Lastly, I take the second polynomial again, and square it, so that -8r becomes +64r^2
And simply stringing them together I have:
9q^2 - 48qr + 64r^2
And that's the answer... and it's worked on quite a few of them like this(polynomials being squared), but not being cubed.
I was just wondering, can somebody help me to determine if this is a common shortcut, or if it even holds true all of the time? I'm worried if I try to use it for problems like that, it may end up failing some of the time, even though it succeeds some of the time.
Oh well... just a simple gradeschool math thread from me... reviewing all my math up to algebra 2 so I can take this stupid GED test. I'm just hoping I can count on this shortcut to be reliable under this certain scenario if I'm presented with any such problems, since I can do it quickly in my head, much faster than doing the FOIL method.
EDIT: I know this is a pretty pointless dumb thread, and the shortcut has only an incredibly limited use, but I dunno... figured I'd make it anyways. And yes, I know... this thread makes me both look and feel stupid.
