Question 83682
<pre><font size = 5><b>
multiply using the vertical method: 
(2r-3s)(4r^2+6rs+9s^2) What is the vertical 
method? Please help ;0/

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Write the longer factor first, the shorter
underneath to line up with the last two terms
of the longer factor, then draw a line underneath: 

                  4r²  +    6rs +   9s²
                  <u>           2r -   3s </u>
                                         
Multiply the -3s by the +9s² and write -27s³ 
on the far right under he line
                                             
                    
                  4r²  +    6rs +   9s²
                  <u>           2r -   3s </u>
                                -  27s³

Multiply the -3s by the +6rs and write -18rs² 
just to the left of the -27s³
       

                  4r²  +    6rs +   9s²
                  <u>           2r -   3s </u>
                       -  18rs² -  27s³
                                 
Multiply the -3s by the 4r² and write -12r²s 
just to the left of the -18rs²                                         

                  4r²  +    6rs +   9s²
                  <u>           2r -   3s </u>
             -  12r²s  -  18rs² -  27s³
                                 
Now we make a new row:

Multiply the 2r by the +9s² and write +18rs² 
directly underneath the -18rs²:

                  4r²  +    6rs +   9s²
                  <u>           2r -   3s </u>
             -  12r²s  -  18rs² -  27s³
                       +  18rs²

                                 
Multiply the 2r by the 6rs and write +12r²s 
just to the left of the +18rs²
  
                                       
                  4r²  +    6rs +   9s²
                  <u>           2r -   3s </u>
             -  12r²s  -  18rs² -  27s³
             +  12r²s  +  18rs²  
                                         
Multiply the 2r by the 4r² and write 8r³ 
just to the left of the +12r²s

                  4r²  +    6rs +   9s²
                  <u>           2r -   3s </u>
             -  12r²s  -  18rs² -  27s³
        8r³  +  12r²s  +  18rs²  
                                          
Now draw a line underneath:

                  4r²  +    6rs +   9s²
                  <u>           2r -   3s </u>
             -  12r²s  -  18rs² -  27s³
        <u>8r³  +  12r²s  +  18rs²________</u>
                                          
Now combine each column vertically.  Begin by
bringing down the -27s³ under the line:

                  4r²  +    6rs +   9s²
                  <u>           2r -   3s </u>
             -  12r²s  -  18rs² -  27s³
        <u>8r³  +  12r²s  +  18rs²________</u>
                                -  27s³

Now combine the -18rs² and the +18rs² and write
+0rs² underneath their column:


                  4r²  +    6rs +   9s²
                  <u>           2r -   3s </u>
             -  12r²s  -  18rs² -  27s³
        <u>8r³  +  12r²s  +  18rs²________</u>
                       +   0rs² -  27s³

Now combine the -12r²s and the -12r²s and write
+0r²s underneath their column:

                  4r²  +    6rs +   9s²
                  <u>           2r -   3s </u>
             -  12r²s  -  18rs² -  27s³
        <u>8r³  +  12r²s  +  18rs²________</u>
             +   0r²s  +   0rs² -  27s³

Finally bring down the 8x³


                  4r²  +    6rs +   9s²
                  <u>           2r -   3s </u>
             -  12r²s  -  18rs² -  27s³
        <u>8r³  +  12r²s  +  18rs²________</u>
        8r³  +   0r²s  +   0rs² -  27s³

and you're done with the vertical 
multiplication.  Now you simplify the
answer by erasing the two 0 terms and
write the final answer as:
              
           8r³ - 27s³

Edwin</pre>