document.write( "Question 1037988: Multiply to find the expanded form of each product
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Algebra.Com's Answer #652674 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Make a Pascal's triangle down to the line that starts with 1 4\r\n" );
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document.write( "Start with this.\r\n" );
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document.write( "    1\r\n" );
document.write( "   1 1\r\n" );
document.write( "  1   1\r\n" );
document.write( " 1     1\r\n" );
document.write( "1       1\r\n" );
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document.write( "Add the two 1's on the second row and place it underneath\r\n" );
document.write( "them on the third row:\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     1\r\n" );
document.write( "1       1 \r\n" );
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document.write( "Add the 1 and the 2 on the 2nd row getting 3 \r\n" );
document.write( "and place the 3 between them on the 3rd row\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   1\r\n" );
document.write( "1       1 \r\n" );
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document.write( "Add the 2 and the 1 on the 3rd row getting 3 \r\n" );
document.write( "and place the 3 between them on the 4th row \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       1\r\n" );
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document.write( "Add the 1 and the 3 on the 4th row getting 4 \r\n" );
document.write( "and place the 4 between them on the 5th row \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     1\r\n" );
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document.write( "Add the 3 and the 3 on the 4th row getting 6 \r\n" );
document.write( "and place the 6 between them on the 5th row \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   1\r\n" );
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document.write( "Add the 3 and the 1 on the 4th row getting 4 \r\n" );
document.write( "and place the 4 between them on the 5th row \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" );
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document.write( "I'll just do the last one:\r\n" );
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document.write( "3. (a + b)4\r\n" );
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document.write( "Take the bottom line of Pascal's triangle:\r\n" );
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document.write( "1     4     6     4     1\r\n" );
document.write( "1a b +4a b +6a b +4a b +1a b   <-- put in \"a, space, b\"\r\n" );
document.write( "1a4b +4a3b +6a2b +4a1b +1a b   <-- put in a's exponents 4,3,2,1,0\r\n" );
document.write( "1a4b0+4a3b1+6a2b2+4a1b3+1a0b4  <-- put in b's exponents 0,1,2,3,4 \r\n" );
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document.write( "Now you can erase the 1's and b0 and a0\r\n" );
document.write( "because they are just 1's, too:\r\n" );
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document.write( " a4  +4a3b +6a2b2+4a b3+   b4 \r\n" );
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document.write( "and close up the spaces:\r\n" );
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document.write( "a4+4a3b+6a2b2+4ab3+b4\r\n" );
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document.write( "Do the others the same way with the upper rows of \r\n" );
document.write( "Pascal's triangle.\r\n" );
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document.write( "Always use the row that has for its second number \r\n" );
document.write( "(after the 1) the exponent of (a+b).\r\n" );
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document.write( "Edwin
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