document.write( "Question 864944: Factorise the following (polynomial):
\n" ); document.write( "(a+b)^3-(a-b)^3 \n" ); document.write( "
Algebra.Com's Answer #521407 by ben720(159)\"\" \"About 
You can put this solution on YOUR website!
First, lengthen the exponent:
\n" ); document.write( "\"%28a%2Bb%29%28a%2Bb%29%28a%2Bb%29-%28a-b%29%28a-b%29%28a-b%29\"
\n" ); document.write( "To find (a+b)(a+b)(a+b), find all the multiplications and add them:
\n" ); document.write( "a*a*a
\n" ); document.write( "a*a*b
\n" ); document.write( "a*b*a
\n" ); document.write( "a*b*b
\n" ); document.write( "b*a*a
\n" ); document.write( "b*a*b
\n" ); document.write( "b*b*a
\n" ); document.write( "b*b*b
\n" ); document.write( "for a total of \"a%5E3%2Ba%5E2b%2Ba%5E2b%2Bab%5E2%2Ba%5E2b%2Bab%5E2%2Bab%5E2%2Bb%5E3\", or \"a%5E3%2B3a%5E2b%2B3ab%5E2%2Bb%5E3\"\r
\n" ); document.write( "\n" ); document.write( "For (a-b)(a-b)(a-b), it's the same, except the terms with exactly 1 or 3 b's will be negative.
\n" ); document.write( "The total of (a-b)(a-b)(a-b) is \"a%5E3-3a%5E2b%2B3ab%5E2-b%5E3\"
\n" ); document.write( "
\n" ); document.write( "Because you're subtracting the second, your number is
\n" ); document.write( "\"%28a%5E3%2B3a%5E2b%2B3ab%5E2%2Bb%5E3%29-%28a%5E3-3a%5E2b%2B3ab%5E2-b%5E3%29\"
\n" ); document.write( "Distribute the -1
\n" ); document.write( "\"a%5E3%2B3a%5E2b%2B3ab%5E2%2Bb%5E3-a%5E3%2B3a%5E2b-3ab%5E2%2Bb%5E3\"
\n" ); document.write( "Combine like terms
\n" ); document.write( "\"6a%5E2b%2B2b%5E3\" \n" ); document.write( "
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