Simplifying Algebraic Expressions and Solving Equations

Introduction

Algebra is a cornerstone of GCSE Maths. From simplifying expressions to solving equations, mastering these skills is essential for exam success.

In this article, we’ll focus on:

1. Simplifying algebraic expressions.
2. Solving linear and quadratic equations.
3. Real-life applications of algebra.

1. Simplifying Algebraic Expressions

   Combining Like Terms

   Terms with the same variable and power can be added or subtracted.

   Example: Simplify .

   • Combine like terms:

      

   • Final answer: .

   Expanding Brackets

   Multiply each term inside the bracket by the term outside.

   Example: Expand .

      

   Factorising Expressions

   Factorising reverses expansion.

   Example: Factorise .

   1. Find the common factor: .
   2. Write as .

2. Solving Linear Equations

   Linear equations have the form .

   Steps to Solve:

   1. Isolate : Undo addition or subtraction.
   2. Divide by the coefficient of .

   Example: Solve .

   1. Subtract 2: .
   2. Divide by 3: .

3. Solving Quadratic Equations

   Quadratics have the form .

   Methods:

   1. Factorisation:

      • Example: Solve .
      • Factorise: .
      • Solutions: .

   2. Quadratic Formula:

         

Practice Question

Question: Solve .

Solution:

1. Subtract 5: .
2. Divide by 2: .

Conclusion

Simplifying expressions and solving equations are key algebraic skills for GCSE Maths. Practice consistently to strengthen your understanding and excel in exams.

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