Before going to study Algebraic Expression, we need to know about term.

Term in Basic Algebra :

Numerical numbers alone or literal numbers alone ortheir combinations by operation of multiplication (or division) are called terms.

Here even if you don't mention division, it is okbecause division is nothing but multiplying with reciprocal.

Examples: 3, -7, 2⁄5, a , x , abc , 6n, -8p, xy , m⁄6 are all terms.

In 2⁄5, 2 is divided by 5. (or we can say 2 is multiplied by 1⁄5)

similarly, In m⁄6, m is divided by 6. (or we can say m is multiplied by 1⁄6)

A combination of terms obtained by the operations of '+' or '-' or bothis called an algebraic expression.

We may also say thatThe several parts of an algeraic expression seperated by '+' or '-' signare called the TERMS of the expression.

Examples:

(i) 5a + 3b, (ii) 4x - 7yz, (iii) 2p + 3q - 3r⁄5, (iv) lx⁄2 + my⁄3 - nz are all Algebraic Expressions.

Example (i) is obtained by adding the terms 5a and 3b .

Example (iv) is obtained by combining the terms lx⁄2, my⁄3 and nz , using '+' and '-' symbols.

while writing the terms we write them with thier sign of '+' or '-'. Since + is the default sign, it need not be written for the term. But '-' is to be written specifically.

For example, The terms of example (ii) are 4x and -7yz. The terms of example (iii) are 2p, 3q and -3r⁄5.

Note that multiplication and division do not seperate terms. Where as addition and subtraction seperate terms.

Thus, xy or x⁄y is one term, while x + y or x - y are two terms.

Factors of a term in Algebra Terms:

When numbers and literals are multiplied to form a product, theneach quantity multiplied is called a factor of the product.A constant factor is called a numerical factor whilea variable factor is called a literal factor.

Example on Algebra Terms :

consider the algebraic expression 7xy - 6a^{2}b. There are two terms: 7xy and -6a^{2}b.

In the first term 7xy :The numerical factor is 7. The literal factors are x, y, xy.

In the second term -6a^{2}b:The numerical factor is -6. The literal factors are a, a^{2}, b , ab and a^{2}b.

Constant Term of Algebra Terms :

A term of the expression having no literal factor is called the constant term.

Examples:

In the expression 2x - y + 8, the constant term is 8.

In the expression 2x^{2} - 2y^{2} + xy - 9, the constant term is -9.

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In a product containing two or more factors, each factor is calledthe coefficient of the product of other factors. In particular, the constant part is called the numerical coefficient of the term and the remaining part is called the literal coefficient of the term.

Example:

In the term 7xy,

Numerical coefficient of the term = 7. Literal coefficient of the term = xy. Coefficient of xy = 7. Coefficient of x = 7y. Coefficient of y = 7x.

When the numerical coefficient of a term is +1 or -1,it will not be written.