Algebraic Expressions

• Introduction

  • What is Algebra?
    • Use of letters/variables to represent unknown numbers
    • Bridge between arithmetic and advanced mathematics
  • Constant
    • Fixed numerical value (e.g., $5, -7, \frac{3}{4}$)
  • Variable
    • Takes changing numerical values
    • Represented by letters like $x, y, z, m, n$

• Terms of an Expression

  • Formation of Expressions
    • Combination of constants and variables connected by operations ($+, -, \times, \div$)
    • Example: $4x + 5$
  • Parts of a Term
    • Factors: Numbers or variables multiplied to form a term (e.g., factors of $3xy$ are $3, x, y$)
    • Coefficient: Numerical factor of a term (e.g., coefficient of $-5xy$ is $-5$)

• Types of Algebraic Expressions

  • Monomial
    • Expression with one term (e.g., $7xy$)
  • Binomial
    • Expression with two terms (e.g., $a + b$)
  • Trinomial
    • Expression with three terms (e.g., $x^2 + 2x - 3$)
  • Polynomial
    • Expression with one or more terms with non-negative integer exponents

• Like and Unlike Terms

  • Like Terms
    • Terms having the same algebraic factors
    • Example: $7xy$ and $-2xy$
  • Unlike Terms
    • Terms having different algebraic factors
    • Example: $7xy$ and $7x^2$
  • Importance
    • Only like terms can be added or subtracted

• Addition and Subtraction of Algebraic Expressions

  • Method of Addition
    • Group like terms together
    • Add numerical coefficients of like terms
    • Example: $(7xy + 5) + (3xy - 2) = 10xy + 3$
  • Method of Subtraction
    • Change the signs of all terms of the expression to be subtracted
    • Add to the first expression

• Finding the Value of an Expression

  • Process of Substitution
    • Replace variables with given numerical values
    • Evaluate using arithmetic rules (BODMAS)
  • Example
    • Find value of $4x - 3$ when $x = 2$
    • Solution: $4(2) - 3 = 8 - 3 = 5$

• Using Algebraic Expressions (General Formulas)

  • Perimeter Formulas
    • Perimeter of a square = $4s$ ($s$ = side)
    • Perimeter of a rectangle = $2(l + b)$ ($l$ = length, $b$ = breadth)
  • Number Patterns
    • Generalizing rules for matchstick patterns (e.g., pattern 'T' needs $2n$ matchsticks)