An algebraic expression is an expression composed of various components, such as variables, constants, coefficients, and arithmetic operations. These components form various parts of the algebraic expressions.
For example:
- 3x + 5
- 2a2 ā 4b + 7
- 5(x + 2) ā 3
Note: The highest power of the variable is known as the degree.
There are many types of algebraic expressions based on the number of terms such as:
- Monomial (1 term: 3x, 5a2)
- Binomial (2 terms: x + 2, 4y - 7)
- Trinomial (3 terms: x2 + 3x + 5, 2a - 4b + 7)
- Multinomial (more than 3 terms: 2x2y + 3xy2 ā 4z - 2, 5a3b ā 2a2b2 + 7ab ā 3)
- Polynomial (general term for expression with multiple terms: 3x3 + 2x2 ā x + 4, 5a4 ā 3a3 + 2a2 ā a + 1)
Based on the degree of polynomial, we can classify them as:
- Constant Expression (Degree 0: 5, ā3, etc.)
- Linear Expression (Degree 1: 3x + 2, 5a - 4b, etc.)
- Quadratic Expression (Degree 2: x2 + 3x + 2, 2y2 - 3y - 5, etc.)
- Cubic Expression (Degree 3: x3 ā 2x2 + x ā 5, 3a3 ā 2a + 7, etc.)
- Quartic Expression (Degree 4: 2x4 ā 3x3 + 5x2 ā 7x + 1, āx4 + 6x2 ā 4x + 8, etc.)
Note: Polynomial is a general term for any expression with multiple terms i.e., all the different types of expressions are polynomial but not the vice versa.
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