### Theory:

Types of terms
We studied that terms are either variable or numbers or a single number and variables multiplied together. Terms are separated by an algebraic operation like addition, subtraction.

The algebraic expression can be a single term or double term or more than two terms. That we can classify the terms based on their expression. That is:
• Monomial
• Binomial
• Trinomial
• Polynomial
Let's understand to learn this classification individually.
1. Monomial:

An algebraic expression with only one term is called a monomial.
Example:
$\begin{array}{l}x,\\ \mathit{xy},\\ {y}^{2}x,\\ -4\mathit{ab},\\ 10\mathit{xz},\\ 19{a}^{3}{b}^{2}c,\\ -24\mathit{xy}.\end{array}$
Above all terms are single terms, so it is called a monomial.
2. Binomial :

An algebraic expression with two terms is called binomial.
Example:
$\begin{array}{l}\mathit{2xy}\phantom{\rule{0.147em}{0ex}}+4\mathit{yz}.\\ \\ \mathit{Here}\phantom{\rule{0.147em}{0ex}}\mathit{2xy}\phantom{\rule{0.147em}{0ex}}\mathit{is}\phantom{\rule{0.147em}{0ex}}\mathit{one}\phantom{\rule{0.147em}{0ex}}\mathit{term},\phantom{\rule{0.147em}{0ex}}\mathit{and}\phantom{\rule{0.147em}{0ex}}4\mathit{yz}\phantom{\rule{0.147em}{0ex}}\mathit{is}\phantom{\rule{0.147em}{0ex}}\mathit{the}\phantom{\rule{0.147em}{0ex}}\mathit{other}\phantom{\rule{0.147em}{0ex}}\mathit{term}.\\ \\ \mathit{Which}\phantom{\rule{0.147em}{0ex}}\mathit{means}\phantom{\rule{0.147em}{0ex}}\mathit{the}\phantom{\rule{0.147em}{0ex}}\mathit{above}\phantom{\rule{0.147em}{0ex}}\mathit{terms}\phantom{\rule{0.147em}{0ex}}\mathit{is}\phantom{\rule{0.147em}{0ex}}\mathit{binomial}.\end{array}$
Further examples are,

$\begin{array}{l}{\mathit{6y}}^{2}x\phantom{\rule{0.147em}{0ex}}-8{x}^{2}y,\\ 10-4\mathit{ab},\\ 10\mathit{xz}+4,\\ 19{a}^{3}+{b}^{2}c,\\ {z}^{2}-24\mathit{xy}.\end{array}$
3. Trinomial :

An algebraic expression with three terms is called a trinomial.
Example:
$\begin{array}{l}\mathit{2xy}\phantom{\rule{0.147em}{0ex}}+4\mathit{yz}-6\mathit{xz}\\ \\ \mathit{Here}\phantom{\rule{0.147em}{0ex}}\mathit{2xy}\phantom{\rule{0.147em}{0ex}}\mathit{is}\phantom{\rule{0.147em}{0ex}}\mathit{one}\phantom{\rule{0.147em}{0ex}}\mathit{term},4\mathit{yz}\phantom{\rule{0.147em}{0ex}}\mathit{is}\phantom{\rule{0.147em}{0ex}}\mathit{the}\phantom{\rule{0.147em}{0ex}}\mathit{second}\phantom{\rule{0.147em}{0ex}}\mathit{term},\phantom{\rule{0.147em}{0ex}}\mathit{and}\phantom{\rule{0.147em}{0ex}}-6\mathit{xz}\phantom{\rule{0.147em}{0ex}}\mathit{is}\phantom{\rule{0.147em}{0ex}}\mathit{the}\phantom{\rule{0.147em}{0ex}}\mathit{third}\phantom{\rule{0.147em}{0ex}}\mathit{term}.\\ \\ \mathit{This}\phantom{\rule{0.147em}{0ex}}\mathit{expression}\phantom{\rule{0.147em}{0ex}}\mathit{contains}\phantom{\rule{0.147em}{0ex}}3\phantom{\rule{0.147em}{0ex}}\mathit{terms},\phantom{\rule{0.147em}{0ex}}\mathit{so}\phantom{\rule{0.147em}{0ex}}\mathit{it}\phantom{\rule{0.147em}{0ex}}\mathit{called}\phantom{\rule{0.147em}{0ex}}\mathit{as}\phantom{\rule{0.147em}{0ex}}\mathit{trinomial}.\end{array}$
Further examples are,

$\begin{array}{l}{\mathit{6y}}^{2}x\phantom{\rule{0.147em}{0ex}}-8{x}^{2}y-12{z}^{2}x\\ 10-4\mathit{ab}+8c\\ 10\mathit{xz}+4-11\mathit{xy}\\ 19{-a}^{3}+{b}^{2}c,\\ {z}^{2}-24+\mathit{xy}.\end{array}$
4. Polynomial:

An algebraic expression with one or more than one terms is called a polynomial.

All the expression of monomial, binomial and trinomial are called as a polynomial.
Example:
$\begin{array}{l}\mathit{xy}\\ \mathit{2abc}\\ \mathit{2xy}\phantom{\rule{0.147em}{0ex}}+4\mathit{yz}-6\mathit{xz}+10\mathit{xyz}\\ {\mathit{6y}}^{2}x\phantom{\rule{0.147em}{0ex}}-8{x}^{2}y-12{z}^{2}x+14{x}^{2}{y}^{2}{z}^{2}\\ 10-4\mathit{ab}+8c\\ 10\mathit{xz}+4-11\mathit{xy}\\ 19{-a}^{3}+{b}^{2}c,\\ {z}^{2}-24+\mathit{xy}.\end{array}$