document.write( "Question 665017: I need to factor x to the 6th minus y to the 6th two different ways. I know to use the difference of squares and the difference of cubes but I need to see the solution. Thank you in advance. \n" ); document.write( "

Algebra.Com's Answer #413638 by kevwill(135) $\"\"$ $\"About$

You can put this solution on YOUR website!
Using the difference of squares:
\n" ); document.write( " $\"x%5E6+-+y%5E6+=+%28x%5E3%29%5E2+-+%28y%5E3%29%5E2\"$
\n" ); document.write( " $\"x%5E6+-+y%5E6+=+%28x%5E3+%2B+y%5E3%29+%2A+%28x%5E3+-+y%5E3%29\"$
\n" ); document.write( "Each of these terms can be factored using the sum of cubes formula and the difference of cubes formula, so
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\n" ); document.write( "Using the difference of cubes:
\n" ); document.write( " $\"x%5E6+-+y%5E6+=+%28x%5E2%29%5E3+-+%28y%5E2%29%5E3\"$
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\n" ); document.write( " $\"x%5E6+-+y%5E6+=+%28x%5E2+-+y%5E2%29+%2A+%28x%5E4+%2B+x%5E2y%5E2+%2B+y%5E4%29\"$
\n" ); document.write( "The first term can be factored using the difference of squares formula:
\n" ); document.write( " $\"x%5E6+-+y%5E6+=+%28x+%2B+y%29+%2A+%28x+-+y%29+%2A+%28x%5E4+%2B+x%5E2y%5E2+%2B+y%5E4%29\"$
\n" ); document.write( "And if you deduced that $\"x%5E4+%2B+x%5E2y%5E2+%2B+y%5E4\"$ can be factored into $\"%28x%5E2+%2B+xy+%2B+y%5E2%29+%2A+%28x%5E2+-+xy+%2B+y%5E2%29\"$ you'd be correct, so
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