# Monomials

A **monomial** is the simplest algebraic expression; it is formed by the product of numbers and letters or variables (with powers) .

It has two parts: the number part is called **coefficient**, and the letters part is called **literal part**.

Examples:

· -4x (-4 is the coefficient and x is the literal part)

· 3xy^{2}z^{5} (3 is the coefficient and xy2z5 is the literal part)

· 4x/y isn’t a monomial

The** degree of a variable** is the index of its power and the **degree of the monomial** is the addition of the degrees of its variables.

Examples: 4x has degree 1 and 3xy^{2}z^{5} has degree 8.

Two monomials are called **similar or like monomials** if they have the same literal part.

Examples:

**Exercise**: Decide if the following expressions are monomials or not, and if they are monomials find their coefficients, literal parts and degrees:

a) -3xy^{3}z^{9}

b) πa^{7}b^{9}c

c) 3x + y

d) 17x/y

e) 4a^{11}b^{3}c^{2}d

Solutions: a) coefficient: -3, literal part: xy^{3}z^{9}; degree: 13; b) coeff.: π, lit. p.: a^{7}b^{9}c, deg: 17; c) it isn't monomial; d) it isn't monomial;

e) coeff.: 4, lit. p.: a^{11}b^{3}c^{2}d , deg: 17

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