document.write( "Question 818731: 125c^6-8d^6 factor completely \n" ); document.write( "

Algebra.Com's Answer #492810 by jsmallt9(3758) $\"\"$ $\"About$

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$\"125c%5E6-8d%5E6\"$
\n" ); document.write( "The greatest common factor (GCF) is 1 (which we rarely bother factoring out).

\n" ); document.write( "Next we try other factoring methods. One of these other methods is to use factoring patterns. And one of these patterns is:
\n" ); document.write( " $\"a%5E3-b%5E3+=+%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29\"$
\n" ); document.write( "This pattern can be used on our expression because $\"125c%5E6\"$ is a perfect cube, $\"%285c%5E2%29%5E3\"$ , and $\"8d%5E6\"$ is also a perfect cube, $\"%282d%5E2%29%5E3\"$ . Using this pattern we get:
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\n" ); document.write( "which simplifies to:
\n" ); document.write( " $\"%285c%5E2-2d%5E2%29%2825c%5E4%2B10c%5E2+%2A+d%5E2%2B4d%5E4%29\"$
\n" ); document.write( "Neither of these factors will factor further, no matter which method we try, so we are finished.
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