Terms of an Algebraic Expression

To learn about the terms of an algebraic expression let us recall the definition of algebraic expression.

We know an algebraic expression is a collection or combination of constant and variables of one or more terms, which are separated by the fundamental operations (+, –, × and ÷).

Some of the examples of algebraic expression are 7b + 5m, 5x + 3y + 10, 5x/y + 3, x + y + z, etc.

Terms of an algebraic expression:

Each part of an algebraic expression which are separated by plus sign (+) or minus sign (-) is called the term of an algebraic expression.

It’s important to remember that the division sign (÷) or multiplication sign (×) does not separate the terms of an algebraic expression.

Examples of algebraic expressions and their terms:

(i)  x + 10

We observe that the number of terms used in the expression x + 10 is 2. The terms are x and 10.

(ii)  5m + 2n - 7

We observe that the number of terms used in the expression 5m + 2n – 7 is 3. The terms are 5m, 2n and 7.

(iii)  3a/b

We observe that the number of term used in the expression 3a/b is 1. The term is 3a/b.

(iv) 3xy + 7xz + 2yz - 6

We observe that the number of terms used in the expression 3xy + 7xz + 2yz - 6 is 4. The terms are 3xy, 7xz, 2yz and 6.

(v)  2abc + 1

We observe that the number of terms used in the expression 2abc + 1 is 2. The terms are 2abc and 1.

Therefore, the algebraic expressions are either simple or compound.

(i) Simple algebraic expressions consist of one term.

(ii) Compound algebraic expressions consist of two or more terms.

Constant term of an algebraic expression:

A term of an algebraic expression which has a fixed numerical value in all situations and does not have any variable is called the constant term of an algebraic expression.

For examples, in the algebraic expression 5x + 2y + xy + 10, 10 is the constant term of the expression.

Types of Algebraic Expressions

Degree of a Polynomial

Subtraction of Polynomials

Power of Literal Quantities

Multiplication of Two Monomials

Multiplication of Polynomial by Monomial

Multiplication of two Binomials

Division of Monomials

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