1. Introduction
Algebraic expressions come in different forms depending on how many terms they have. Understanding these types helps students classify expressions correctly and makes it easier to perform operations like addition, subtraction, and multiplication.
In this topic, we will learn the main types of algebraic expressions such as monomials, binomials, trinomials, and polynomials.
2. What is an Algebraic Expression?
An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, or division.
Examples:
- \(5x + 3\)
- \(2y - 7\)
- \(3ab + 4a - 9\)
3. Classification Based on Number of Terms
An algebraic expression can have one term, two terms, three terms, or more. Based on this count, the expressions are classified as follows:
3.1. Monomial
A monomial is an expression with exactly one term. It may contain variables and constants but has no plus or minus sign inside.
Examples:
- \(5x\)
- \(-3y^2\)
- \(7abc\)
- \(9\)
3.2. Binomial
A binomial has exactly two terms. These terms are separated by a plus or minus sign.
Examples:
- \(3x + 4\)
- \(a - b\)
- \(5m - 2n\)
3.3. Trinomial
A trinomial has three terms.
Examples:
- \(2x + 3y + 4\)
- \(a + b + c\)
- \(m^2 - m + 6\)
3.4. Polynomial
A polynomial is an expression that has one or more terms. It includes monomials, binomials, trinomials, and expressions with more terms.
Examples:
- \(x^3 + 2x + 1\)
- \(4a - 7b + 9c - 2\)
- \(3p^2 - p + 8\)
4. Degree of an Algebraic Expression
The degree of an algebraic expression is the highest power of the variable(s) in the expression.
Examples:
- Degree of \(5x^3\) is 3.
- Degree of \(4x^2 + 3x + 1\) is 2.
- Degree of \(7ab\) is 2 because \(a^1 b^1 = 1 + 1 = 2\).
4.1. Degree Table
| Expression | Degree |
|---|---|
| \(3x\) | 1 |
| \(4x^2 - 7\) | 2 |
| \(2xy\) | 2 (1 + 1) |
| \(6a^2 b^3\) | 5 (2 + 3) |
5. Standard Form of an Expression
An expression is in standard form when the terms are written in order of decreasing powers.
Example:
- Expression: \(3x + 5x^3 + 2x^2\)
- Standard form: \(5x^3 + 2x^2 + 3x\)
5.1. Why Standard Form Helps
Standard form is useful because:
- It makes expressions easier to compare.
- It helps in finding the degree quickly.
- It is required when solving equations.
6. Examples and Practice
Try to classify the following expressions:
- \(7x\)
- \(3a - 2b\)
- \(4x + y - 9\)
- \(2p^2 + 5p + 3\)
- \(9m - 4n + 2k - 1\)
7. Summary
- A monomial has one term.
- A binomial has two terms.
- A trinomial has three terms.
- A polynomial can have one or more terms.
- The degree of an expression is the highest power of its variable(s).
- Standard form arranges terms from highest power to lowest.