Some Other Types of Expression

We have other expressions, also Apart from monomial, binomial, and polynomial types of expressions which are  

• Numeric Expression
• Variable Expression

Numeric Expression

An expression that consists of only numbers and operations but never includes any variable is termed a numeric expression.

Some of the examples of numeric expressions are 11 + 5, 14 ÷ 2, etc.

Variable Expression

An expression that contains variables along with numbers and operations to define an expression is termed a variable expression.

Some examples of a variable expression include 5x + y, 4ab + 33, etc.

Some algebraic formulae

1. (a + b)² = a² + 2ab + b²
2. (a – b)² = a² – 2ab + b²
3. (a + b)(a – b) = a² – b²
4. (x + a)(x + b) = x² + x(a + b) + ab
5. (a + b)³ = a³ + b³ + 3ab(a + b)
6. (a – b)³ = a³ – b³ – 3ab(a – b)  
7. a³ – b³ = (a – b)(a² + ab + b²)
8. a³ + b³ = (a + b)(a² – ab + b²)

There are some terms of algebraic expression which are basically used. Examples of using these terms:

If 2x² + 3xy + 4x + 7 is an algebraic expression.

Then, 2x², 3xy, 4x, and 7 are the Terms

Coefficient of the term: 2 is the coefficient of x²

Constant term: 7

Variables: here x, y are variables

Factors of a term: If 2xy is a term, then its factors are 2, x, and y.

Exponent Rules

Exponents formulas are expressed as:

1. a⁰ = 1
2. a¹ = a
3. a^m × aⁿ = a^m+n
4. a^m/aⁿ = a^m−n
5. a^−m = 1/a^m  
6. (a^m)ⁿ = a^mn
7. (ab)^m = a^mb^m
8. (a/b)^m = a^m/b^m
9. a^1/m = ^m√a

The basic concept of algebra taught us how to express an unknown value using letters such as x, y, z, etc.  These letters are termed here as variables. This expression can be a combination of both variables and constants.  Any value that is placed before and multiplied by a variable is termed a coefficient. An idea of expressing numbers using letters or alphabets without specifying their actual values is termed an algebraic expression.