An expression consisting of __arithmetic__ numbers, letters (used as symbols) and __operation signs__ is called an __Algebraic Expression__

*Examples:*

2x + 3y , -9p + 2r, x^{2} + 5x + 6, a^{3} + b^{3} + 3ab^{2} + 3a^{2}b

**2. Constant:**

Algebraic symbols that have a fixed value and do not change like __variables__ (which are used as __place holders__) are called __Constants__

*Examples:*

In 2x + 3y + 4, 4 is a **constant**. In 2a^{2} – 3ab + 7, 7 is a **constant**

**3. Variable**

A symbol in Algebra that can be plugged in with different __numerical values__ (numbers) is called a __variable__

In 5p + 6q + r, the letters (**symbols**)* p,q* are called **Variables**.

Note: 5p + 6q + r is also a variable, since any number can be plugged in for p, q and r as required.

**4 .Terms of an expression**

The parts in an algebraic expression connected by the
operation signs ** + or — ** are called __Terms__

In 2y + 3, 2y is one term and 3 is another term.

**5. Monomials**

An algebraic expression containing only one term is called a __Monomial__. Monomials are also called simple expressions.

2x, 5x^{2} , pq are examples of monomials.

**6. Binomial**

An algebraic expression that contains two terms is called a __Binomial __

2x + 3y, 2p^{2} + 9y^{3} are some examples of Binomials.

**7. Trinomial**

An algebraic expression that has three terms is called a __Trinomial__.

3x + 4y + 5z, ax^{2} + bx + c are examples of Trinomials.

**8. Polynomial**

An algebraic expression that contains one term, two terms, three terms or more is called a __Polynomial__.

By this definition, each of monomial, binomial and trinomial is a Polynomial.

Examples of Polynomials are:

3x, 4y^{2}, pq, (which are Monomials)

3x + 4y, 5q + 9t, -m^{2} – n^{2} (which are Binomials)

ax^{2} + bx + c, 3a - b + (5/3) c. (which are Trinomials)

**9. Factor:**

Symbols or Numbers in multiplication are called __factors__.

Example:

In pq, p and q are factors in the multiplication
**p × q**.

pq is called the product of the factors p and q.

Example:

2 and 3 are factors in the multiplication 2×3 which is equal
to 6.

2 and 3 are called __Numerical Factors__

6 is called the product of
2 and 3.

In the product *xy*, x and y are the factors and *xy* is called the product of x and y.

x and y are called **Literal Factors.**

**10. Coefficient:**

__Coefficient__ is of two types. Numerical coefficient and Literal coefficient.

**Numbers** form __Numerical coefficients__ and **symbols** form __literal coefficients__.

Examples:

In 2xy, 2 is the number or the Numerical coefficient while xy, the symbol, is the Literal Coefficient.

In the Monomial* y*, the Numerical coefficient is 1
and the literal coefficient is * y*

In the product 100xy, 100 is the Numerical coefficient and xy is the literal coefficient.

**11. Like Terms:**

Two or more terms that have the same literal coefficients are called __Like Terms__. Like terms can have
different Numerical Coefficients, but not literal coefficients.

Examples:

4pq and 100pq are like terms as the literal coefficients xy are same in the two terms.

-13p^{2}q^{2} and 13 p^{2}q^{2} are Like terms as only the numerical coefficients are different but the literal coefficients are same.

**12. Unlike Terms**

Terms that are not Like terms are __Unlike Terms__.

So, Unlike terms have different literal coefficients.

Examples

3xy, 3xy^{2} are unlike terms