Explanation:
In algebra, like terms are terms that have the same variables and powers.
The coefficients do not need to match. (Our solved example in
mathguru.com uses this concept)
Unlike terms are two or more terms that are not like terms, i.e. they do not
have the same variables or powers. The order of the variables does not matter
unless there is a power. For example, 8xyz^{2} and −5xyz^{2} are like terms because they have the
same variables and power while 3abc and
3ghi are unlike terms
because they have different variables. Since the coefficient doesn't affect
likeness, all constant terms are like terms.
Combination
If all terms in an expression are like terms, the expression can be simplified, or rewritten as
a fraction or equation for mathematical purposes. For example, 2a, 2a are the
same number and variable making it a like term.
http://en.wikipedia.org/wiki/Like_terms
Polynomial
In mathematics, a polynomial (from Greek poly, "many" and medieval
Latin binomium, "binomial") is an expression of finite length constructed from variables (also known as indeterminates)
and constants, using only the
operations of addition, subtraction, multiplication, and non-negative integer exponents.
Overview
A polynomial
is either zero, or can be written as the sum of one or more non-zero terms. The number of terms is
finite. These terms consist of a
constant (called the coefficient of the term) which may be multiplied by a finite number of variables (usually represented by
letters). Each variable may have an exponent that is a non-negative integer,
i.e., a natural number. The exponent on
a variable in a term is called the degree of that variable in that term,
the degree of the term is the sum of the degrees of the variables in that term,
and the degree of a polynomial is the largest degree of any one term. Since x = x^{1}, the degree of a variable
without a written exponent is one. A term with no variables is called a constant term, or just a
constant. The degree of a constant term is 0.
Two
terms with the same variables raised to the same powers are called "like
terms". Polynomials are added using the commutative, associative,
and distributive laws, by combining like terms. For example, if
Then
which can be simplified to
(Our solved example in mathguru.com uses
this concept)
http://en.wikipedia.org/wiki/Polynomial
The above explanation is copied from
Wikipedia, the free encyclopedia and is remixed as allowed under the Creative
Commons Attribution- ShareAlike 3.0 Unported License.