Notes On Understanding Algebraic Expressions - CBSE Class 7 Maths

Expressions that contain only constants are called numeric or arithmetic expressions. It is a set of numerical values that are separated by the four mathematical operations, addition, subtraction, multiplication and division.
e.g. 9 + 8, 5 – 3

Expressions that contain constants and variables, or just variables, are called algebraic expressions. Variables and constants are combined using mathematical operations to form an algebraic expression.
e.g. x – 5, 3b – 6

While writing algebraic expressions, we do not write the sign of multiplication. An algebraic expression containing only variables also has the constant 1 associated with it. The parts of an algebraic expression added to form the expression are called its terms.
e.g. The number of terms in the expression x2 + 3x + 5 is 3. 

A term that contains variables is called a variable term. A term that contains only a number is called a constant term.

The constants and the variables whose product makes a term of an algebraic expression, are called the factors of the term. The factors of a constant term in an algebraic expression are not considered. The numerical factor of a variable term is called its coefficient. If the coefficient of a term is 1, it is usually omitted. If the coefficient of a term is –1, it is indicated by only the minus sign. The variable factors of a term are called its algebraic factors.

Terms that have different algebraic factors are called unlike terms. Terms that have the same algebraic factors are called like terms. We can compare only the like terms.The unlike terms can not be compared.

Algebraic expressions that contain only one term are called monomials. Algebraic expressions that contain two unlike terms are called binomials. Algebraic expressions that contain three unlike terms are called trinomials. All algebraic expressions that have one or more terms are called polynomials. Therefore, monomials, binomials and trinomials are also polynomials.

Summary

Expressions that contain only constants are called numeric or arithmetic expressions. It is a set of numerical values that are separated by the four mathematical operations, addition, subtraction, multiplication and division.
e.g. 9 + 8, 5 – 3

Expressions that contain constants and variables, or just variables, are called algebraic expressions. Variables and constants are combined using mathematical operations to form an algebraic expression.
e.g. x – 5, 3b – 6

While writing algebraic expressions, we do not write the sign of multiplication. An algebraic expression containing only variables also has the constant 1 associated with it. The parts of an algebraic expression added to form the expression are called its terms.
e.g. The number of terms in the expression x2 + 3x + 5 is 3. 

A term that contains variables is called a variable term. A term that contains only a number is called a constant term.

The constants and the variables whose product makes a term of an algebraic expression, are called the factors of the term. The factors of a constant term in an algebraic expression are not considered. The numerical factor of a variable term is called its coefficient. If the coefficient of a term is 1, it is usually omitted. If the coefficient of a term is –1, it is indicated by only the minus sign. The variable factors of a term are called its algebraic factors.

Terms that have different algebraic factors are called unlike terms. Terms that have the same algebraic factors are called like terms. We can compare only the like terms.The unlike terms can not be compared.

Algebraic expressions that contain only one term are called monomials. Algebraic expressions that contain two unlike terms are called binomials. Algebraic expressions that contain three unlike terms are called trinomials. All algebraic expressions that have one or more terms are called polynomials. Therefore, monomials, binomials and trinomials are also polynomials.

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