Algebraic Expressions
Constants
A symbol having a fixed numerical value is called a constant. It does not vary.
Examples : 9, -6, √2, π etc.
Variables
A symbol which can be assigned different numerical value is called a variable.
Example : Circumference of a circle is given by C = 2πr, where r is the radius of the circle. Here, 2 and π are constants while C and r are variables.
Algebraic Expressions
An algebraic expression is a combination of constants and variables joined together by the algebraic operations of addition, subtraction, multiplication, and division.
Example : 5x2 -9x + 4 is an algebraic expression. Here, 5, 2, -9 and 4 are constants while x is a variable..
Terms of an Algebraic Expression
The several parts of an algebraic expression separated by + or – operations are called the terms of the expression.
Example : 5x2 -9x + 4 is an algebraic expression containing three terms, namely 5x2, -9x and 4.
Evaluation of Algebraic Expressions
Any variable in an algebraic expression may take on or be assigned different values. When values of variables change, the value of the algebraic expression changes. To evaluate an algebraic expression means to determine the value of the expression for a given value of each variable in the expression. Replace each variable in the expression with the given value, then simplify the resulting expression using the order of operations. If the algebraic expression contains more than one variable, replace each variable with its assigned value and simplify the expression as before.
Q. List the constants and variables for each algebraic expression.
Q. Evaluate each expression for the given values.
Simplification of Algebraic Expressions
Sometimes an algebraic expression can be simplified to make it easier to evaluate or to use in some other way. To do so, we use the properties of real numbers. We can use the same properties in formulas because they contain algebraic expressions.
Q. Simplify each given algebraic expression.
