Degree of Monomial

A monomial is an algebraic expression that consists of:

Variables (like x, y, z) with their exponents

A numerical coefficient No addition, subtraction, or division operations

The degree of a monomial is determined by adding together all the exponents of variables in that term. It represents the total power of all variables combined. Key points about degree of a monomial:

1. For single variable monomials:

The exponent of that variable is its degree Example: x³ has degree 3

2. For multiple variable monomials:

Add all the exponents of different variables Example: x²y³ has degree 5 (2 + 3 = 5)

3. Constants:

Any constant number has degree 0 Example: 5 has degree 0

4. Coefficient doesn't affect degree:

The numerical coefficient is not included in degree calculation Example: 3x²y³ and x²y³ both have degree 5

For the example in the 9x²y²

Exponent of x is 2

Exponent of y is 2

Total degree = 2 + 2 =

Standard Form of an Algebraic Expression is a way of writing expressions where:

Primary Rule - Descending Order of Degrees:

Terms are arranged from highest degree to lowest degree

Example: 3x + 5x² - 9

Standard form: 5x² + 3x - 9 (Rearranged by degree)

Here:

5x² has degree

3x has degree

-9 has degree

Secondary Rule - Alphabetical Order:

When terms have the same degree, arrange them alphabetically

Example: 3c + 6a - 2b

Standard form: 6a - 2b + 3c (Alphabetical)

Here all terms have degree , so we arrange them as a, b, c

Examples with Explanations:

1. Example (3x + 5x² - 9):

Original degrees:

3x → degree

5x² → degree

-9 → degree

Standard form: 5x² + 3x - 9

Now arranged in descending order of degrees: , 1,

2. Example (3c + 6a - 2b):

All terms have degree

Since degrees are same, use alphabetical order

Standard form: 6a - 2b + 3c

Terms arranged as: , b,