Download Adding/Subtracting Monomials

Operations with Monomials
Adding/Subtracting Monomials
Multiplying Monomials
RULE: When you add monomials, you must have “like” terms. RULE: When you multiply monomials, you __________________
You __________________________ coefficients and
coefficients and ________________ exponents.
___________________ exponents.
Example:
1) 3x2 + 4x2 + 5x _______________________
Example:
1) (3x)(4x)(5x)(- 2x2) ________________________
2) 4xy3 + 5x2y3 – 7x2y3 ______________________
2) (4xy)(-2xy3)(3x2y3) _________________________
3) x2 + 3x – 5 + x2 – 7x – 2 _______________________
3) (7ab)(-5a2b3) ______________________________
Power to Power Monomials
RULE: When you raise monomials to a power, you
_________________ the coefficients to a
___________________ and _________________ exponents.
Dividing Monomials
RULE: When you divide
monomials you ___________
coefficients and ____________
exponents.
Negative Exponents:
NEVER, EVER, EVER
LEAVE A NEGATIVE
EXPONENT
RULE:
3
2) (-2x2y3)2 __________________________
1) 14 x2 ________________
7x
Think of it as “canceling like terms”
3) (-3a2y4)3 ____________________________
2)
1) (3x) _______________________
2 x 2 y 3
_____________
8 x 4 y 5
 2x3
3)  4
 6y
3

 ____________

 If an exponent is negative in the
numerator, you move it to the
_________________ and make it
positive.
 If an exponent is negative in the
denominator, you move it to the
______________________ and
make it positive.
 If the exponent is outside a set of
parenthesis – flip the fraction and
make the exponent positive
Operations with Monomials
Putting it all together!!!! A monomial expression is in simplified form when:
1) There are no powers of powers,
2) Each base appears only once,
3) All fractions are in simplest form, and
4) There are NO NEGATIVE EXPONENTS!!
1)
v 3
2)  2
w
(2 x 3 y 4 )(3x 2 y 5 )
( x 2 y 3 )(12 x 5 y 6 )
_______________________
3a 3b 2
3)
16a 2 b 3
4) (a 3b 3 )( ab) 2
___________________________
____________________________
_________________________________
5) (2r s ) (3rs )
30a 2 b 6
6)
60a 6 b 8
(a 2 b 3 c 4 )(6ab 2 ) 2
7)
(4abc 3 ) 2 (a 2 b 2 c)
 x2 
8)  3 
 3y 
________________
_________________
___________________
2 3 3
 3x 
9)  
 2y 
2 1
3
  3x 4
10) 
2
 6y
______________



1
 2x 2 y 5
11)  4 7
 3x y
_________________
3
_______________________



3
_________________