SOLUTION: Can you help me solve the following problem. It is to Factor the polynomial completely. {{{192k^3m-375m^4}}} I really appriciate it. I am not getting this section at all.

Algebra ->  Functions -> SOLUTION: Can you help me solve the following problem. It is to Factor the polynomial completely. {{{192k^3m-375m^4}}} I really appriciate it. I am not getting this section at all.      Log On


   

Question 121497: Can you help me solve the following problem. It is to Factor the polynomial completely.
192k%5E3m-375m%5E4
I really appriciate it. I am not getting this section at all.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Factor:
192k%5E3m-375m%5E4 In this problem, it would be nice if the binomial were a difference of two cubes so that it could be factored as shown in my answer to your previous problem. Notice that each term of the binomial has a common factor of m, and you should be able to see that the coefficients of each term are both divisble by 3 (The sum of the digits is divisble by 3), so you can first factor out 3m:
192k%5E3m-375m%5E4+=+3m%2864k%5E3-125m%5E3%29
Now, using the fact that a binomial that is the difference of two cubes can be factored: A%5E3-B%5E3+=+%28A-B%29%28A%5E2%2BAB%2BB%5E2%29, you can apply this to your problem:
3m%2864k%5E3-125m%5E3%29+=+3m%28%284k%29%5E3-%285m%29%5E3%29=3m%284k-5m%29%28%284k%29%5E2%2B%284k%29%285m%29%2B%285m%29%5E2%29 Simplifying, we get:
3m%284k-5m%29%2816k%5E2%2B20km%2B25m%5E2%29 and you could factor the trinomial a little more...
16k%5E2%2B20km%2B25m%5E2+=+16k%5E2%2B5%284km%2B5m%5E2%29, so finally, you get:
192k%5E3m-375m%5E4+=+3m%284k-5m%29%2816k%5E2%2B5%284km%2B5m%5E2%29%29