What is Algebra?

Algebra is a branch of mathematics that uses letters (variables) to represent unknown values. Known values are called constants. Together, they form expressions and equations.

Example:

• Expression: $2x+5$
• Equation: $2x+5=15$

Here, $x$ is the variable, and solving gives $x=5$.

Basic Algebraic Operations

Algebra combines variables and constants using four operations:

Operation	Symbol	Example
Addition	+	$x+7$
Subtraction	–	$x-3$
Multiplication	×	$4x$
Division	÷	$\frac{x}{2}$

Order of Operations (BODMAS Rule)

When solving algebraic expressions, follow BODMAS:

• Brackets
• Orders (powers, roots)
• Division
• Multiplication
• Addition
• Subtraction

Example: $2+3x\times (4-2)=2+3x\times 2=2+6x$

Key Algebraic Formulas

• $(a+b{)}^2=a^2+2ab+b^2$
• $(a-b{)}^2=a^2-2ab+b^2$
• $(a+b)(a-b)=a^2-b^2$

These formulas simplify calculations and are widely used in exams.

Solving Equations

Steps to solve:

1. Simplify both sides.
2. Move variables to one side.
3. Move constants to the other side.
4. Solve for the variable.

Example: $2x+5=15$ → $2x=10$ → $x=5$

Real-Life Applications of Algebra

• Finance: Interest calculation, budgeting.
• Science: Chemical equations, physics formulas.
• Technology: Algorithms, coding.
• Daily Life: Comparing prices, planning schedules.

Common Mistakes

• Forgetting BODMAS order.
• Misplacing negative signs.
• Mixing constants and variables incorrectly.
• Not simplifying fractions in equations.

Conclusion

Basic algebra is more than just math — it’s a problem-solving tool used in academics, careers, and everyday life. By mastering operations, formulas, and equations, students can build strong analytical skills and prepare for advanced mathematics.