7. ADDING AND SUBTRACTING
MONOMIALS AND POLYNOMIALS
Monomials
•
The letters and exponents never change; only the numbers out front change.
Whatever letters are in the problem are the same in the answer.
•
Like terms? (same letters and exponents)
if YES
The letters and exponents stay the same in the
answer. We just add or subtract the numbers out
front.
if NO
Circle it; this is the answer.
Examples
3x + 2y
can’t add since the
letters are not the same
!
5x + 7x
5 + 7 = 12
12x
3x + 2y
!!
"7xy " 2xy
!
!
!
5a 2b + 2ab 2
can’t add since the
exponents are not the same
"7 " +2
"7 + "2
"9
!
"9xy
5a 2b + 2ab 2
!
"3x 2 y " 5yx 2 !
!
"3 " +5
"3 + "5
"8
!
"8x 2 y or " 8yx 2
!
!
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Created by J. Shahom (February 2005)
Adding Polynomials
• Line up like terms vertically (up and down) and use the rules for adding and
subtracting monomials.
Examples
(6x 2 " x + 1) + ("x 2 + x " 2)
Add " 4 x 2 + 6x + 2 to x 2 + 3x " 4.
6x 2 "1x + 1
"4 x 2 + 6x + 2
+1x 2 + 3x " 4
!
!
"3x 2 + 9x " 2
"1x 2 + 1x " 2
5x 2 + 0x "1
5x 2 "1
!
!
Subtracting Polynomials
!
Strategy: Change it into an addition problem.
!
!
1) The foam (“from”) goes to the top of the soda.
2) Stay – Change – Change
Numbers
up top
stay the
same
Change to
addition
Change the
sign of all
numbers in
the bottom
3) Add the polynomials.
Example
Subtract " 6x 2 + 5x " 3
from 2x 2 + 7x " 9.
1. “from” goes to the top
!
2x 2 + 7x " 9
2. Stay-Change-Change
"("6x 2 + 5x " 3)
2x 2 + 7x " 9
+ (6x 2 " 5x + 3)
3. Add
2x 2 + 7x " !
9
!
+ 6x 2 " 5x + 3
8x 2 + 2x " 6
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!
Created by J. Shahom (February 2005)
!