# Algebriac Expressions

**Algebraic Expressions:**

For e.g. **4x ^{2}+3**,

**7y**, etc.

^{2}-2y+3The 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 (**4x ^{2}**) and (

**3**).

Now consider the send expression above, which can be written as

**7y ^{2} +(-2y) + 3**

therefore, the terms of the expression are (**7y ^{2}**), (

**-2y**) and (

**3**). Note, the minus sign (-) is included in the term.

**Factors of a term:**

For the expression **7y ^{2}-2y+3**, the terms are (

**7y**), (

^{2}**-2y**) and (

**3**). The term 7y

^{2}is the product of 7, y and y; we therefore say that 7, y and y are factors of the term 7y

^{2}. A term is a product of its factors.

The term -2y is the product of the factors -2 and y or 2 and -y.

**Coefficients:**

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, x^{2} - 2y, etc.

An algebraic expression which contains three terms is called a **trinomial**; for example a + b + 2, 7x^{2} - 3x + 4, etc.

In general, an expression with one or more terms is called a **polynomial**.