document.write( "Question 1034947: Find the 6th term of (-4a+3b)^13 \n" ); document.write( "
Algebra.Com's Answer #649581 by ikleyn(52790)\"\" \"About 
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document.write( "  1-st term               2-nd term              3-rd term             4-th term             5-th term            6-th term\r\n" );
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document.write( "\"C%5B13%5D%5E0%2A%28-4a%29%5E13%2A%283b%29%5E0\"   \"C%5B13%5D%5E1%2A%28-4a%29%5E12%2A%283b%29%5E1\"   \"C%5B13%5D%5E2%2A%28-4a%29%5E11%2A%283b%29%5E2\"   \"C%5B13%5D%5E3%2A%28-4a%29%5E10%2A%283b%29%5E3\"   \"C%5B13%5D%5E4%2A%28-4a%29%5E9%2A%283b%29%5E4\"   \"C%5B13%5D%5E5%2A%28-4a%29%5E8%2A%283b%29%5E5\"\r\n" );
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document.write( "The 6-th term is \"C%5B13%5D%5E5%2A%28-4a%29%5E8%2A%283b%29%5E5\"  (the general formula is  \"C%5Bn%5D%5Ek%2A%28-4a%29%5E%28n-k%29%2A%283b%29%5Ek\",  k = 0 (first term), 1 (the 2-nd term), 2 (the 3-rd term), . . . ).\r\n" );
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document.write( "Or, after simplifying, \"C%5B13%5D%5E5%2A%28-4a%29%5E8%2A%283b%29%5E5\" = \"C%5B13%5D%5E5%2A4%5E8%2A3%5E5%2Aa%5E8%2Ab%5E5\" = \"1287%2A4%5E8%2A3%5E5%2Aa%5E8%2Ab%5E5\" = \"20495794176%2Aa%5E8%2Ab%5E5\".\r\n" );
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document.write( "\"C%5B13%5D%5E5\" = \"%2813%21%29%2F%285%21%2A8%21%29\" = \"%2813%2A12%2A11%2A10%2A9%29%2F%281%2A2%2A3%2A4%2A5%29\" = 1287  is the number of combination 13 things taken 5 at a time.\r\n" );
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document.write( "On combinations, see the lesson Introduction to Combinations in this site.\r\n" );
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document.write( "On binomial expansion see the lesson Binomial Theorem, Binomial Formula, Binomial Coefficients and Binomial Expansion.\r\n" );
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