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
2r - 3s
Multiply the -3s by the +9s² and write -27s³
on the far right under he line
4r² + 6rs + 9s²
2r - 3s
- 27s³
Multiply the -3s by the +6rs and write -18rs²
just to the left of the -27s³
4r² + 6rs + 9s²
2r - 3s
- 18rs² - 27s³
Multiply the -3s by the 4r² and write -12r²s
just to the left of the -18rs²
4r² + 6rs + 9s²
2r - 3s
- 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
2r - 3s
- 12r²s - 18rs² - 27s³
+ 18rs²
Multiply the 2r by the 6rs and write +12r²s
just to the left of the +18rs²
4r² + 6rs + 9s²
2r - 3s
- 12r²s - 18rs² - 27s³
+ 12r²s + 18rs²
Multiply the 2r by the 4r² and write 8r³
just to the left of the +12r²s
4r² + 6rs + 9s²
2r - 3s
- 12r²s - 18rs² - 27s³
8r³ + 12r²s + 18rs²
Now draw a line underneath:
4r² + 6rs + 9s²
2r - 3s
- 12r²s - 18rs² - 27s³
8r³ + 12r²s + 18rs²________
Now combine each column vertically. Begin by
bringing down the -27s³ under the line:
4r² + 6rs + 9s²
2r - 3s
- 12r²s - 18rs² - 27s³
8r³ + 12r²s + 18rs²________
- 27s³
Now combine the -18rs² and the +18rs² and write
+0rs² underneath their column:
4r² + 6rs + 9s²
2r - 3s
- 12r²s - 18rs² - 27s³
8r³ + 12r²s + 18rs²________
+ 0rs² - 27s³
Now combine the -12r²s and the -12r²s and write
+0r²s underneath their column:
4r² + 6rs + 9s²
2r - 3s
- 12r²s - 18rs² - 27s³
8r³ + 12r²s + 18rs²________
+ 0r²s + 0rs² - 27s³
Finally bring down the 8x³
4r² + 6rs + 9s²
2r - 3s
- 12r²s - 18rs² - 27s³
8r³ + 12r²s + 18rs²________
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