document.write( "Question 83682: multiply using the vertical method:\r
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Algebra.Com's Answer #60184 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "multiply using the vertical method: \r\n" );
document.write( "(2r-3s)(4r^2+6rs+9s^2) What is the vertical \r\n" );
document.write( "method? Please help ;0/\r\n" );
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document.write( "Write the longer factor first, the shorter\r\n" );
document.write( "underneath to line up with the last two terms\r\n" );
document.write( "of the longer factor, then draw a line underneath: \r\n" );
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document.write( "                  4r²  +    6rs +   9s²\r\n" );
document.write( "                             2r -   3s \r\n" );
document.write( "                                         \r\n" );
document.write( "Multiply the -3s by the +9s² and write -27s³ \r\n" );
document.write( "on the far right under he line\r\n" );
document.write( "                                             \r\n" );
document.write( "                    \r\n" );
document.write( "                  4r²  +    6rs +   9s²\r\n" );
document.write( "                             2r -   3s \r\n" );
document.write( "                                -  27s³\r\n" );
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document.write( "Multiply the -3s by the +6rs and write -18rs² \r\n" );
document.write( "just to the left of the -27s³\r\n" );
document.write( "       \r\n" );
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document.write( "                  4r²  +    6rs +   9s²\r\n" );
document.write( "                             2r -   3s \r\n" );
document.write( "                       -  18rs² -  27s³\r\n" );
document.write( "                                 \r\n" );
document.write( "Multiply the -3s by the 4r² and write -12r²s \r\n" );
document.write( "just to the left of the -18rs²                                         \r\n" );
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document.write( "                  4r²  +    6rs +   9s²\r\n" );
document.write( "                             2r -   3s \r\n" );
document.write( "             -  12r²s  -  18rs² -  27s³\r\n" );
document.write( "                                 \r\n" );
document.write( "Now we make a new row:\r\n" );
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document.write( "Multiply the 2r by the +9s² and write +18rs² \r\n" );
document.write( "directly underneath the -18rs²:\r\n" );
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document.write( "                  4r²  +    6rs +   9s²\r\n" );
document.write( "                             2r -   3s \r\n" );
document.write( "             -  12r²s  -  18rs² -  27s³\r\n" );
document.write( "                       +  18rs²\r\n" );
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document.write( "                                 \r\n" );
document.write( "Multiply the 2r by the 6rs and write +12r²s \r\n" );
document.write( "just to the left of the +18rs²\r\n" );
document.write( "  \r\n" );
document.write( "                                       \r\n" );
document.write( "                  4r²  +    6rs +   9s²\r\n" );
document.write( "                             2r -   3s \r\n" );
document.write( "             -  12r²s  -  18rs² -  27s³\r\n" );
document.write( "             +  12r²s  +  18rs²  \r\n" );
document.write( "                                         \r\n" );
document.write( "Multiply the 2r by the 4r² and write 8r³ \r\n" );
document.write( "just to the left of the +12r²s\r\n" );
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document.write( "                  4r²  +    6rs +   9s²\r\n" );
document.write( "                             2r -   3s \r\n" );
document.write( "             -  12r²s  -  18rs² -  27s³\r\n" );
document.write( "        8r³  +  12r²s  +  18rs²  \r\n" );
document.write( "                                          \r\n" );
document.write( "Now draw a line underneath:\r\n" );
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document.write( "                  4r²  +    6rs +   9s²\r\n" );
document.write( "                             2r -   3s \r\n" );
document.write( "             -  12r²s  -  18rs² -  27s³\r\n" );
document.write( "        8r³  +  12r²s  +  18rs²________\r\n" );
document.write( "                                          \r\n" );
document.write( "Now combine each column vertically.  Begin by\r\n" );
document.write( "bringing down the -27s³ under the line:\r\n" );
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document.write( "                  4r²  +    6rs +   9s²\r\n" );
document.write( "                             2r -   3s \r\n" );
document.write( "             -  12r²s  -  18rs² -  27s³\r\n" );
document.write( "        8r³  +  12r²s  +  18rs²________\r\n" );
document.write( "                                -  27s³\r\n" );
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document.write( "Now combine the -18rs² and the +18rs² and write\r\n" );
document.write( "+0rs² underneath their column:\r\n" );
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document.write( "                  4r²  +    6rs +   9s²\r\n" );
document.write( "                             2r -   3s \r\n" );
document.write( "             -  12r²s  -  18rs² -  27s³\r\n" );
document.write( "        8r³  +  12r²s  +  18rs²________\r\n" );
document.write( "                       +   0rs² -  27s³\r\n" );
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document.write( "Now combine the -12r²s and the -12r²s and write\r\n" );
document.write( "+0r²s underneath their column:\r\n" );
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document.write( "                  4r²  +    6rs +   9s²\r\n" );
document.write( "                             2r -   3s \r\n" );
document.write( "             -  12r²s  -  18rs² -  27s³\r\n" );
document.write( "        8r³  +  12r²s  +  18rs²________\r\n" );
document.write( "             +   0r²s  +   0rs² -  27s³\r\n" );
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document.write( "Finally bring down the 8x³\r\n" );
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document.write( "                  4r²  +    6rs +   9s²\r\n" );
document.write( "                             2r -   3s \r\n" );
document.write( "             -  12r²s  -  18rs² -  27s³\r\n" );
document.write( "        8r³  +  12r²s  +  18rs²________\r\n" );
document.write( "        8r³  +   0r²s  +   0rs² -  27s³\r\n" );
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document.write( "and you're done with the vertical \r\n" );
document.write( "multiplication.  Now you simplify the\r\n" );
document.write( "answer by erasing the two 0 terms and\r\n" );
document.write( "write the final answer as:\r\n" );
document.write( "              \r\n" );
document.write( "           8r³ - 27s³\r\n" );
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document.write( "Edwin
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