document.write( "Question 121497: Can you help me solve the following problem. It is to Factor the polynomial completely.\r
\n" ); document.write( "\n" ); document.write( " $\"192k%5E3m-375m%5E4\"$
\n" ); document.write( "I really appriciate it. I am not getting this section at all. \n" ); document.write( "

Algebra.Com's Answer #89187 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Factor:
\n" ); document.write( " $\"192k%5E3m-375m%5E4\"$ 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:
\n" ); document.write( " $\"192k%5E3m-375m%5E4+=+3m%2864k%5E3-125m%5E3%29\"$
\n" ); document.write( "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:
\n" ); document.write( " $\"3m%2864k%5E3-125m%5E3%29+=+3m%28%284k%29%5E3-%285m%29%5E3%29\"$ = $\"3m%284k-5m%29%28%284k%29%5E2%2B%284k%29%285m%29%2B%285m%29%5E2%29\"$ Simplifying, we get:
\n" ); document.write( " $\"3m%284k-5m%29%2816k%5E2%2B20km%2B25m%5E2%29\"$ and you could factor the trinomial a little more...
\n" ); document.write( " $\"16k%5E2%2B20km%2B25m%5E2+=+16k%5E2%2B5%284km%2B5m%5E2%29\"$ , so finally, you get:
\n" ); document.write( " $\"192k%5E3m-375m%5E4+=+3m%284k-5m%29%2816k%5E2%2B5%284km%2B5m%5E2%29%29\"$ \n" ); document.write( "

\n" );