Mathematics Factoring Problem

November 6, 2006 10:33 AM

Mathematics Factoring Problem Factor completely: 16p^8w – 49p^6w The ^ represents an exponent. I know this problem is a difference of two squares, it's the 8w and 6w that throw me off. I've tried several solutions but none check to be true.
posted by foreversport to Education (16 answers total)

factor out p^6w so you have p^6w(16p^2w-49) then you can factor the second part so you have p^6w(4p^w-7)(4p^w+7)
posted by martinX's bellbottoms at 10:41 AM on November 6, 2006

If w=1, then the problem is 16p^8 - 49p^6, the answer is (4p^4 +- 7p^3). Put the w's back in to get (4p^4w +- 7p^3w). The w's don't matter in this case is what I'm saying.
posted by clearlynuts at 10:42 AM on November 6, 2006

aren't there other places you can go for help with your homework? I'm pretty sure a TI-89 can factor stuff like that.
posted by martinX's bellbottoms at 10:44 AM on November 6, 2006

Response by poster: Thanks for the replies. clearlynuts is clearly right!
posted by foreversport at 11:37 AM on November 6, 2006

The w is not in the exponent, then?
posted by notsnot at 12:02 PM on November 6, 2006

Yeah, I agree with notsnot - I thought you had written
16*p^(8w) - 49*p^(6w)
in which case martinX is definitely correct.

Clearlynuts is only correct if the w is not in the exponent - in which case the problem could be rewritten as
16*w*p^8 - 49*w*p^6
= w (16p^8 - 49p^6)
= wp^6(16p^2 - 49)
= wp^6 (4p - 7)(4p + 7)
which is equivalent to what clearlynuts has, if you split the p^6 into p^3 * p^3 and multiply through the brackets.
posted by PercussivePaul at 12:25 PM on November 6, 2006

w is in the exponent. And I am correct as long as w is an integer. I assumed that w was an integer because of the simplicity of the question.
posted by clearlynuts at 1:57 PM on November 6, 2006

You are correct even if w is not an integer. Except as martinX and PP point out, you need to pull out p^6w as a separate factor.

Tip: for clarity, use the  tag to create superscripts. I believe what foreversport was asking for, and the subsequent answer, is:

16p^8w-49p^6w = p^6w(4p^w+7)(4p^w-7)
posted by DevilsAdvocate at 2:20 PM on November 6, 2006

Best answer: I really don't understand the prejudice around here against helping with homework. ISTM that brushing up on this stuff is as good for me as it is for the asker.

16p^8w – 49p^6w
= (4p^4w)² - (7p^3w)²
= (4p^4w + 7p^3w)(4p^4w - 7p^3w)

Which is fine as far as it goes, but you're supposed to factor completely:

= p^3w(4p^w + 7)(4p^w - 7)
posted by flabdablet at 2:31 PM on November 6, 2006

Whoops! DevilsAdvocate is correct; I forgot that p^3w comes out of both factors.
posted by flabdablet at 2:34 PM on November 6, 2006

Clearlynuts' answer can be simplified to my answer, and it works no matter what w is. It just seems kind of silly to use up space for a question that a graphing calculator could have solved.
posted by martinX's bellbottoms at 3:35 PM on November 6, 2006

It just seems kind of silly to use up space for a question that a graphing calculator could have solved.

Booo. The calculator doesn't tell you how to solve a similar problem in the future.
posted by peeedro at 4:04 PM on November 6, 2006

Response by poster: Thanks for all the replies, guys. FYI, I do not have a Ti-89 calculator, nor am I going to purchase one of those expensive things just for this problem. I have a Ti-83+. And based on all the replies this got, I think it's obvious that factoring is good to be brushed up upon by a lot of people!
posted by foreversport at 4:28 PM on November 6, 2006

Here is a free desktop graphing calculator that fits on a floppy for easy distribution. Wikipedia link for the same (which would be more interesting if it introduced the features for students).
posted by Brian B. at 6:27 PM on November 6, 2006

If you're against helping someone with homework, I presume that it's because you believe the point of homework is to learn and not just to get credit. If so, then your suggestion to use a fancy calculator is even less helpful.

I'm all for using AskMeFi, friends and TAs if it facilitates understanding how to solve a problem from first principles.
posted by randomstriker at 6:40 PM on November 6, 2006

My point was not that the asker should begin relying on an expensive calculator, my point was more along the lines that we could fill ask metafilter with homework questions, and that there are better ways to figure this stuff out.
Although my ti-89 definitely saved me during calculus, not because it would just give me the answer, but because I figured out how to use it to check my work step by step, and because I could see the answers to a bunch of similar problems at once by just changing a few numbers, and it made the methods seem clearer.
posted by martinX's bellbottoms at 7:26 PM on November 6, 2006