Expression: Term, Factor and Coefficient

An expression that includes a combination of integral or fractional constants (numbers), variables (alphabets) connected by mathematical operators (such as +, -, ×, ÷) is known as algebraic expression. The value of an algebraic expression depends on variables (having various numerical values) and these expressions contain terms, factors and coefficients which are covered in the ncert class-8 mathematics Chapter-9. Few examples of algebraic expressions are- a+2d, 2x+y, z+4c, etc.

Read Also: Definite Integral Formula

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Expression

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In Mathematics, expression is made up of constants, variables, coefficients and arithmetic operations. If we take some mathematical statements then when we say x is tripled then it is expressed as- 3x, when we say 5 less than z then it is expressed as z-5 and many more.

Lets understand different parts of an algebraic expression with an example-

If we consider an equation- 4x+8y-3

Different parts of the equation are-

Coefficients - 4 is coefficient of x, 8 is coefficient of y and 3 is coefficient of constant term.

Constant - 3

Variables - x and y

Factors- 4 and x are factors of term 1, 8 and y are factors of term 2, 3 is factor of term 3. 

Terms - 4x, 8y and 9

Mathematical operators - (+ and - ).

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Terms

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Terms are the parts of an algebraic expression separated by + or - signs. It can be a single number, a variable, product of two or more variables, or product of a number and variable. An algebraic expression may contain single or more terms. On the basis of the number of terms in algebraic expression, it is classified as a monomial, binomial and trinomial. Here are some examples-

6xy has one term called a monomial.

3y+4x has two terms called binomial.

3x+4y+8 has three terms called polynomials.

Check Important Notes for Integral Calculus

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Factors

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When the numbers and variables are multiplied to form a term then this is called factors. For example in 9xz which is a term having factor 9, x and z, Here 9 is multiplied by x and z. Factorization is the process of expressing the term as a product of 2 or more variables and numbers. For example-

A2 - B2 = (A+B)(A-B), here A+B and A-B are factors of A2 - B2

• The important aspect of the factor is that it can not be further factorized. For example, 8xz is written as a product of 8, x and z neither a product of 8 and xz because xz is further factorized into x and z. 
• 1 is not taken as a factor separately.
• Factor of a2 is a and a. 

Check Also: Differentiation and Integration Formula

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Coefficients

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In an algebraic expression the number(constant) multiplied by a variable or written along with a variable is called a coefficient. The variable which does not contain any constant value has a coefficient of 1. For example- the term x has coefficient 1. The term 6xz has coefficient 6 which is a constant value. 

The term -xy has coefficient -1 and when there is no numerical term and no sign is mentioned before the variable then we take the coefficient as +1.

Read More: Difference Between Parametric and Non-Parametric

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Things to Remember

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• The terms that have the same powers in variables are called like terms for example - 7x3, -8x3, 3x3 
• Terms having variables with different powers are unlike terms for example- 6x2, 3x, -7x4 
• An algebraic expression is made up of terms, variables, constants, factors, and coefficients with operators + or - between them.

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