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Like terms

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, 8xyz2 and −5xyz2 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 = x1, 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