In Algebra, we deal with Relations where some of the values are fixed while others are variable.
The relationship between these fixed & variables values that we study in algebra lead us to what we call algebraic expressions. So, we can define an algebraic expression as a relation between the fixed & the variable values combined together with the help of different mathematical operations, viz., +, -, * & /.
When such values have a bonding of multiplication or division, we get different terms in algebra & these terms when in turn get associated with each other by addition or subtraction they become algebra expression.
For example: 3x/7 + 3y2 – 6xy + 12 is an algebraic expression in which 3x/7, 3y2, – 6xy, 12 are the terms combined together using only ‘+’ or ‘-‘; while the terms in themselves are formed by the multiplication or ‘/’ & division between constants & variables as in 3x/7, 3/7 is a fixed value being multiplied by a variable ‘x’. Similarly in other terms also the values combine by multiplication or / & division.
As we know what terms in algebraic expressions are, we classify these expressions on the basis of number of terms each expression has. Let us know about such classification now.
An expression with only one term is called a monomial. Example: 3a, 29y, 8t, 65 are all monomials.
An expression with two terms is called a binomial. Example, 2x - 3a, 7 + 29y, 5b - 8t, 6m + 5 are all binomials.
An expression with three terms is called a trinomial. Example, 3p + q, 2s - 9t, 35 + 8t, 16y - 5z are all trinomials.
All the expressions with two or more terms are called Polynomials.
Algebraic expression can be defined as expression which is comprised of constants (values that cannot be changed), variables (values that can be changed as required), and a finite number of algebraic operations such as addition, subtraction, multiplication, and power (exponential) etc. In other words, an algebraic expression can be stated as expression...Read More