document.write( "Question 371233: factor the polynomial. 8u^3-125w^3 \n" ); document.write( "

Algebra.Com's Answer #264558 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"8u%5E3-125w%5E3\"$
\n" ); document.write( "When factoring always start with the Greatest Common Factor (GCF). However the GCF here is 1 and we do not often factor out 1's. After the GCF you try any of the other factoring techniques:

Factoring by patterns
Trinomial factoring
Factoring by grouping
Factoring by trial and error of the possible rational roots.

\n" ); document.write( "The keys to factoring this expression are:

Recognizing that $\"8u%5E3\"$ and $\"125w%5E3\"$ are both perfect cubes. $\"8u%5E3+=+%282u%29%5E3\"$ and $\"125w%5E3+=+%285w%29%5E3\"$
Knowing that there is a pattern for a difference of cubes: $\"a%5E3+-+b%5E3+=+%28a-b%29%28a%5E2+%2B+ab+%2B+b%5E2%29\"$

\n" ); document.write( "From this we realize that we can use the pattern, with \"a\" being 2u and \"b\" being 5w:
\n" ); document.write( " $\"%282u-5w%29%28%282u%29%5E2+%2B+%282u%29%285w%29+%2B+%285w%29%5E2%29\"$
\n" ); document.write( "which simplifies to:
\n" ); document.write( " $\"%282u-5w%29%284u%5E2+%2B+10uw+%2B+25w%5E2%29\"$ \n" ); document.write( "

\n" );