document.write( "Question 426811: factor\r
\n" ); document.write( "\n" ); document.write( "625s^6-5f^6\r
\n" ); document.write( "\n" ); document.write( "the correct factorization is? \n" ); document.write( "

Algebra.Com's Answer #296850 by jsmallt9(3758) $\"\"$ $\"About$

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$\"625s%5E6-5f%5E6\"$
\n" ); document.write( "When factoring, always start with the Greatest Common Factor (GCF). The GCF here is 5:
\n" ); document.write( " $\"5%28125s%5E6-f%5E6%29\"$
\n" ); document.write( "Next look to the other methods of factoring:

Patterns
- $\"a%5E2-b%5E2+=+%28a%2Bb%29%28a-b%29\"$
- $\"a%5E2%2B2ab%2Bb%5E2+=+%28a%2Bb%29%28a%2Bb%29+=+%28a%2Bb%29%5E2\"$
- $\"a%5E2-2ab%2Bb%5E2+=+%28a-b%29%28a-b%29+=+%28a-b%29%5E2\"$
- $\"a%5E3%2Bb%5E3+=+%28a%2Bb%29%28a%5E2-ab%2Bb%5E2%29\"$
- $\"a%5E3-b%5E3+=+%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29\"$
Trinomials
Factoring by grouping
Factoring by trial and error of the rational roots

\n" ); document.write( "Since $\"125+=+5%5E3\"$ and since exponents that are multiples of 3 (like 6's) are perfect cubes, the second factor fits the pattern for difference of cubes (the last one above) with the \"a\" being $\"5s%5E2\"$ and the \"b\" being $\"r%5E2\"$ , Using this pattern to factor it we get:
\n" ); document.write( " $\"5%285s%5E2-s%5E2%29%28%285s%5E2%29%5E2%2B%285s%5E2%29%28r%5E2%29%2B%28r%5E2%29%5E2%29\"$
\n" ); document.write( "which simplifies to:
\n" ); document.write( " $\"5%285s%5E2-s%5E2%29%2825s%5E4%2B5s%5E2r%5E2%2Br%5E4%29\"$
\n" ); document.write( "And try as we might (and we should) none of these factors will factor further so we are finished. \n" ); document.write( "

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