Class 7 Chapter 6: Algebraic Expressions

Important Concepts and Formulas

1.      A symbol that can take different values is called a variable.

2.      A symbol having a fixed numerical value is called a constant.

3.      We can form an algebraic expression involving variables and constants using basic operations (+, –, ×, ÷) to connect them. For example, 5xy – 8 is an algebraic expression involving the variables x, y and constants 5 and 8.

4.      The signs ‘+’ and ‘–’ separate the expression into various parts. These parts are called terms.

5.      When terms have the same variables and if the powers of the variables are same, then they are called like terms, else they are unlike terms.

6.      The numerical factor in a term is called its coefficient.

7.      A monomial has 1 term, a binomial has 2 unlike terms and a trinomial has 3 unlike terms.

8.      The degree of a polynomial is the degree of term having the highest exponent (or sum of exponents). For example, the degree of 3x + 2x²y – 7 is 3 (therefore, the term 2x²y has degree as 2 + 1 = 3).

9.      To add or subtract algebraic expressions, we add or subtract the like terms together but keep the unlike terms as such. For example, (5x + 2xy + 7z + y) + (–3y + x – 3xy) = (5x + x) + (2xy – 3xy) + (–3y + y) + (7z) = 6x + (–xy) + (–2y) + 7z or 6x –xy – 2y + 7z.

10. When the value of variable(s) involved in an expression is known, then the value of the expression is obtained by the substitution method. For example, If x = –2 and y = 3, then the value of 4x – 2xy + 8 is 4(–2) – 2(–2) (3) + 8 or –8 + 12 + 8 or 12.