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Add  Subtract POLYNOMIALS
A monomial is an algebraic expression that is a product of a real number and
one or more letters with
whole number exponents . A polynomial is an algebraic sum of monomials. Special
names are given
to polynomials of one, two and three terms ( monomial, binomial, trinomial ) and
all others are simply
called polynomial. The degree of a polynomial in one variable is the highest
power to which the
variable is raised. Polynomials of degree 2 are frequently called “quadratic”
and polynomials of
degree 3 are called “cubic”.
The degree of a monomial in several variables is the sum of the
exponents of each variable. The degree of a polynomial in several variables is the highest degree of the monomials in the polynomial. 
Examples:
Monomials: 2, [degree 0], 3a, [degree 1],
,
[degree 3],
,
[degree 4],
,
[degree 5]
Binomials :
[degree 2],
[degree 2], 3a – 6 [degree 1],
[degree 3]
Trinomials :
[degree 2],
[degree 9]
Addition of Polynomials : To add two or more polynomials use the basic
properties (associative,
commutative, distributive, etc.) and add the coefficients of like terms (or
combine like terms .)
Caution: Like terms must have the same letters
with the same exponents. Do not change exponents when 
Examples:
Apply the associative and commutative properties  
Apply the distributive property.  
Add coefficients. 
Watch signs and note that the middle terms aren’t “similar”.  
Apply the associative and commutative properties.  
Apply the distributive property.  
Add coefficients. 
Negation of a Polynomial: To negate a polynomial multiply each term by (1).
Example:
Subtraction of Polynomials : To subtract a polynomial from another you
must add the “opposite”
(or negate the polynomial following the “minus sign” and add the result
algebraically).
Watch the signs.  
Change to (1) times polynomial  
Distribute the (1) over the 2^{nd} polynomial.  
Apply the associative and commutative properties.  
Add coefficients.  
Watch the signs.  
Change to (1) times polynomial.  
Distribute the (1) over the 2^{nd} polynomial.  
Apply associative and commutative properties.  
Add coefficients.  
Note that the middle terms aren’t “similar”.  
Watch the signs. Change to (1) times polynomial.  
Distribute the (1) over the 2^{nd} polynomial.  
Apply the associative and commutative properties.  
Apply the distributive property.  
Add coefficients. 
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