For e.g. 4x2+3, 7y2-2y+3, etc.
The combination of variables and constants when take part in the formation of mathematical expression, then such an expression is known as Algebraic Expression.
Terms of an expressions:
Terms are added to form expression.
Consider the first expression above, the terms are (4x2) and (3).
Now consider the send expression above, which can be written as
7y2 +(-2y) + 3
therefore, the terms of the expression are (7y2), (-2y) and (3). Note, the minus sign (-) is included in the term.
Factors of a term:
For the expression 7y2-2y+3, the terms are (7y2), (-2y) and (3). The term 7y2 is the product of 7, y and y; we therefore say that 7, y and y are factors of the term 7y2. A term is a product of its factors.
The term -2y is the product of the factors -2 and y or 2 and -y.
Consider the term -2y above. Here -2 is the numerical coefficient or simply the coefficient of the term.
Sometimes, the term may contain more than one variable, for e.g. 24xy. In such a case, the following will hold:
--> 24 is the numerical coefficient
--> 24 is the coefficient of xy
--> 24x is the coefficient of y
--> 24y is the coefficient of x
Like and Unlike Terms:
When terms have the same algebraic factors (i.e., those which contain variables), they are like terms. Examples include: 4x and 5x, 2xy and 7xy, etc.
On the other hand if the terms do not have the same algebraic factors, they are called unlike terms.
Monomials, Binomials, Trinomials and Polynomials:
An algebraic expression with only one term is called a monomial; for example 5x, 7pq, -25z, etc.
An algebraic expression which contains two unlike terms is called binomial; for example, a + b, x2 - 2y, etc.
An algebraic expression which contains three terms is called a trinomial; for example a + b + 2, 7x2 - 3x + 4, etc.
In general, an expression with one or more terms is called a polynomial.