document.write( "Question 1067827: How to factorise: a^3+b^3+3a^2b+3ab^2
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Algebra.Com's Answer #682992 by josgarithmetic(39617) $\"\"$ $\"About$

You can put this solution on YOUR website!
Binomial Theorem? Pascal's Triangle? If you are not sure how to use them for help, try polynomial Division. Divide your cubic expression by $\"a%2Bb\"$ and you should be able to find a quotient which is a more easily factorable quadratic expression.\r
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document.write( "          a^2     2ab       b^2\r\n" );
document.write( "     _______________________________________\r\n" );
document.write( "a+b  |    a^3  +  3a^2*b  +3b^2a  +  b^3\r\n" );
document.write( "     |\r\n" );
document.write( "     |    a^3     a^2*b\r\n" );
document.write( "      ------------------\r\n" );
document.write( "           0      2a^2*b   3b^2*a \r\n" );
document.write( "                  2a^2*b   2a*b^2\r\n" );
document.write( "                 ----------------\r\n" );
document.write( "                    0       ab^2     b^3\r\n" );
document.write( "                            ab^2     b^3\r\n" );
document.write( "                           ---------------\r\n" );
document.write( "                             0        0\r\n" );
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\n" ); document.write( "That quotient is $\"a%5E2%2B2ab%2Bb%5E2\"$ . \n" ); document.write( "

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