Description: Meaning and Basic Terms
Algebraic Expressions
Meaning
- A collection of constants and variables connected by one or more of the operations is called an algebraic expression.
- For example: 3x2 + 5xz2 + 12 is an algebraic expression having 3 terms separated by addition.
Constants
- A symbol which has a fixed value is called a constant.
- Eg. In the expression 2x + 3, the term 3 is the constant
Variables
- A symbol which can be given various numerical values is called a variable.
- In the expression, x = y + 7, x and y are variables.
Types of Expressions
- Monomial - An expression having one term. Eg. 5x2y3
- Binomial - An expression having two terms. Eg. 5x2y3 + 2xy
- Trinomial - An expression having three terms. Eg. 5x2y3 + 2xy + 9
- Multinomial - An expression having two or more terms.
Factors
- Each of the quantity (constant or variable) multiplied together to form a product is called a factor of the product.
- Eg. In the expression 3xy + 5, 5 is the constant factor and 3xy is the variable or literal factor.
Coefficients
- Any factor of a non-constant term in an expression is called the coefficient of the remaining factor of the term.
- Eg. In the expression, 5a2b + 3b, 5 is the coefficient of a2b and 3 is the coefficient of b.
Like Terms
- The terms having exactly the same literals or variables (irrespective of the constant coefficient) are called like terms.
- Eg. 5x2y and 3x2y are like terms.
Unlike Terms
- The terms having different variables are called unlike terms.
- Eg. 5x2y and 3xy2 are unlike terms.
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