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
Additive inverse
In mathematics, the additive
inverse, or opposite,
of a number a is the number that, when added to a,
yields zero. The additive inverse
of F is denoted −F.
For example, the additive inverse of 7 is −7, because 7 +
(−7) = 0, and the additive inverse of −0.3 is 0.3, because
−0.3 + 0.3 = 0.
In other words, the additive inverse of a number is the number's
negative. For example, the additive inverse of 8 is −8, the additive
inverse of 10002 is −10002 and the additive inverse of x² is −(x²).
http://en.wikipedia.org/wiki/Additive_inverse
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)
In
general any expression can be considered to be a polynomial if it is built up
from variables and constants using only addition, subtraction, multiplication,
and raising expressions to constant positive whole number powers.
Since
subtraction can be replaced by addition of the opposite quantity (Our solved example in mathguru.com uses this concept) and since positive whole number exponents can be
replaced by repeated multiplication, all polynomials can be constructed from
constants and variables using only addition and multiplication.
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.