Algebraic Expressions

Quick Revision Notes: Algebraic Expressions

Class 7 - Mathematics (MP Board)

---

1. Introduction to Basic Concepts

• Constant (अचर): A quantity that has a fixed numerical value.
  • Examples: 7, -5, 3/4, π
• Variable (चर): A quantity that does not have a fixed value; it can take various numerical values. Variables are usually denoted by letters of the English alphabet like x, y, z, a, b, m, etc.
  • Examples: In 5x, x is the variable.
• Algebraic Expression (बीजीय व्यंजक): A combination of constants and variables connected by the signs of fundamental arithmetic operations (+, -, ×, ÷).
  • Examples: 4x + 5, 3xy - 7, 2z^2 - 3z + 1

---

2. Terms, Factors, and Coefficients

• Terms (पद): The parts of an algebraic expression which are added or subtracted are called terms.
  • Example: In the expression 4x + 5y - 3, the terms are 4x, 5y, and -3.
• Factors (गुणनखंड): The individual quantities that are multiplied to form a term are called its factors.
  • Example: In the term 5xy, the factors are 5, x, and y.
• Coefficient (गुणांक): The numerical factor of a term is called its numerical coefficient (or simply coefficient).
  • Example: In the term -7xy, the numerical coefficient is -7.

---

3. Types of Algebraic Expressions

Based on the number of terms present in an expression, they are classified as:

1. Monomial (एकपदी व्यंजक): An expression containing only one term.
   • Examples: 7x, -5y^2, 3
2. Binomial (द्विपदी व्यंजक): An expression containing two unlike terms.
   • Examples: a + b, 5x - 3, 4l^2 - 3m
3. Trinomial (त्रिपदी व्यंजक): An expression containing three unlike terms.
   • Examples: ax + by + c, x^2 - 5x + 6
4. Polynomial (बहुपदी व्यंजक): An expression containing one or more terms with non-negative integer exponents of variables. (All monomials, binomials, and trinomials are polynomials).

---

4. Like and Unlike Terms

• Like Terms (समान पद): Terms that have the same algebraic factors (the variables and their exponents are identical). Only their numerical coefficients can differ.
  • Examples: 4x and -7x are like terms; ab^2 and 2ab^2 are like terms.
• Unlike Terms (असामान पद): Terms that do not have the same algebraic factors.
  • Examples: 4x and 4y; 5x^2 and 5x are unlike terms.

Important Rule: We can add or subtract only like terms. Unlike terms cannot be added or subtracted to form a single term.

---

5. Addition and Subtraction of Algebraic Expressions

• Addition: Group all the like terms together and then add their numerical coefficients while keeping the common algebraic part unchanged.
  • Example: Add (7x + 4) and (3x - 2). = (7x + 3x) + (4 - 2) = 10x + 2
• Subtraction: Change the sign of each term of the expression to be subtracted (positive becomes negative, negative becomes positive), and then add it to the first expression by grouping like terms.
  • Example: Subtract (2x - 5) from (5x + 3). = (5x + 3) - (2x - 5) = 5x + 3 - 2x + 5 = (5x - 2x) + (3 + 5) = 3x + 8

---

6. Finding the Value of an Expression

To find the value of an algebraic expression, substitute the given numerical values for the variables in the expression and perform the arithmetic operations according to standard rules (BODMAS).

• Example: Find the value of 2x - 3 when x = 4.
  • Substitute x = 4:
  • = 2(4) - 3
  • = 8 - 3 = 5

---

7. Using Algebraic Expressions (Patterns and Formulas)

Algebra is widely used to write formulas and mathematical patterns in a concise way.

• Perimeter of a square with side s: P = 4s
• Perimeter of a rectangle with length l and breadth b: P = 2(l + b)
• Area of a square with side s: A = s^2
• Area of a rectangle with length l and breadth b: A = l × b