document.write( "Question 1033282: What is the binomial expansion of (2x - 1)^5 as a polynomial in simplest form? \n" ); document.write( "
Algebra.Com's Answer #647870 by Edwin McCravy(20056)\"\" \"About 
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document.write( "(2x-1)5 has 5+1 or 6 terms.\r\n" );
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document.write( "Construct Pascal's triangle down to the 6th line,\r\n" );
document.write( "the one that starts \"1   5\".  Each line starts and\r\n" );
document.write( "ends with 1 and every number is gotten by adding\r\n" );
document.write( "two adjacent numbers to get the number between and\r\n" );
document.write( "below.  For instance the 2 in the third line is\r\n" );
document.write( "gotten by adding the two 1's above it and on each\r\n" );
document.write( "side of it. The 3 on the 4th line is gotten by\r\n" );
document.write( "adding the 1 and 2 just above it.\r\n" );
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document.write( "          1\r\n" );
document.write( "        1   1\r\n" );
document.write( "      1   2   1\r\n" );
document.write( "    1   3   3   1\r\n" );
document.write( "  1   4   6   4   1    \r\n" );
document.write( "1   5  10  10   5   1  \r\n" );
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document.write( "That 6 numbers on the bottom line are the \"binomial \r\n" );
document.write( "coefficients\" of the 6 terms.  Incidentally, they are \r\n" );
document.write( "also the combinations of 5 things taken 0 through 5 at \r\n" );
document.write( "a time.\r\n" );
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document.write( "Notice below the pattern of exponents of the two terms \r\n" );
document.write( "(2x) and (-1) carefully how one starts at 5 and goes \r\n" );
document.write( "down to 0 and the other starts and 0 and goes up to 5:\r\n" );
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document.write( "1(2x)5(-1)0+5(2x)4(-1)1+10(2x)3(-1)2+10(2x)2(-1)3+5(2x)1(-1)4+1(2x)0(-1)5\r\n" );
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document.write( "Simplify those 6 terms by using ordinary rules of exponents\r\n" );
document.write( "and multiplication of algebra, remembering that (-1) raised to\r\n" );
document.write( "an even power is +1 and when raised to an odd power is -1 which\r\n" );
document.write( "makes the signs alternate between + to -:\r\n" );
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document.write( "32x5-80x4+80x3-40x2+10x-1\r\n" );
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document.write( "Edwin

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