document.write( "Question 213846: 64x^6 - 1\r
\n" ); document.write( "\n" ); document.write( "Im confused. \n" ); document.write( "
Algebra.Com's Answer #161555 by nerdybill(7384)\"\" \"About 
You can put this solution on YOUR website!
Remember, if you saw:
\n" ); document.write( "(a^2 - b^2)
\n" ); document.write( "It's called \"difference of squares\"
\n" ); document.write( "When you see this you should automatically know that the factors are:
\n" ); document.write( "(a+b)(a-b)
\n" ); document.write( ".
\n" ); document.write( "Similarly:
\n" ); document.write( "64x^6 - 1
\n" ); document.write( "Can be written as:
\n" ); document.write( "(8x^3)^2 - (1)^2
\n" ); document.write( "Now, you have a \"difference of squares\" -- leading you to factor it as:
\n" ); document.write( "(8x^3 + 1)(8x^3 - 1)
\n" ); document.write( ".
\n" ); document.write( "Wait, you're still not done. Notice, the above can be rewritten as:
\n" ); document.write( "((2x)^3 + 1^3)((2x)^3 - 1^3)
\n" ); document.write( "Now you have a \"sum of cubes\" and a \"difference of cubes... these are special factoring cases:
\n" ); document.write( "((2x)^3 + 1^3) can be rewritten as:
\n" ); document.write( "(2x + 1)(4x^2 - 2x + 1)
\n" ); document.write( "and
\n" ); document.write( "((2x)^3 - 1^3) can be rewritten as:
\n" ); document.write( "(2x - 1)(4x^2 + 2x + 1)
\n" ); document.write( ".
\n" ); document.write( "This means instead of:
\n" ); document.write( "((2x)^3 + 1^3)((2x)^3 - 1^3)
\n" ); document.write( "we can rewrite as:
\n" ); document.write( "(2x + 1)(4x^2 - 2x + 1)(2x - 1)(4x^2 + 2x + 1)\r
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\n" ); document.write( "\n" ); document.write( "Reference, for further reading:
\n" ); document.write( "http://www.purplemath.com/modules/specfact.htm
\n" ); document.write( "http://www.purplemath.com/modules/specfact2.htm\r
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