REVISION NOTES
IGCSE Edexcel Mathematics A
2.2 Algebraic Manipulation
2.2.1 Evaluate expressions by substituting numerical values for letters
2.2.2 Collect like terms
2.2.3 Multiply a single term over a bracket
![edexcel_igcse_mathematics a_topic 13_algebraic manipulation_001_expanding single brackets](https://resource.studiaacademy.com/wp-content/uploads/2022/05/edexcel_igcse_mathematics-a_topic-13_algebraic-manipulation_001_expanding-single-brackets-1.png)
2.2.4 Take out common factors
2.2.5 Expand the product of two simple linear expressions
![edexcel_igcse_mathematics a_topic 13_algebraic manipulation_005_Algebraic Fractions: Linear (2)](https://resource.studiaacademy.com/wp-content/uploads/2022/05/edexcel_igcse_mathematics-a_topic-13_algebraic-manipulation_005_Algebraic-Fractions_-Linear-2.png)
2.2.6 Understand the concept of a quadratic expression and be able to factorise such expressions (limited to x² + bx + c)
Factorising is the reverse process of expanding.
![edexcel_igcse_mathematics a_topic 13_algebraic manipulation_006_Completing the Square (a = 1)](https://resource.studiaacademy.com/wp-content/uploads/2022/05/edexcel_igcse_mathematics-a_topic-13_algebraic-manipulation_006_Completing-the-Square-a-1-.png)
2.2.7 Manipulate algebraic fractions where the numerator and/or the denominator can be numeric, linear or quadratic (Higher Tier Only)
Some equations contain fractional coefficients. A good approach is to multiply the whole equation by a positive whole number, to clear the fractions away.
![](https://resource.studiaacademy.com/wp-content/uploads/2022/05/edexcel_igcse_further-pure-maths_fpm_topic-02_the-quadratic-function_007_quadratic-formula-07.png)
![edexcel_igcse_mathematics a_topic 13_algebraic manipulation_008_Algebraic Fractions: Quadratic (3)](https://resource.studiaacademy.com/wp-content/uploads/2022/05/edexcel_igcse_mathematics-a_topic-13_algebraic-manipulation_008_Algebraic-Fractions_-Quadratic-3.png)
2.2.8 Complete the square for a given quadratic expression (Higher Tier Only)
![edexcel_igcse_mathematics a_topic 13_algebraic manipulation_007_Completing the Square (a ≠ 1)](https://resource.studiaacademy.com/wp-content/uploads/2022/05/edexcel_igcse_mathematics-a_topic-13_algebraic-manipulation_007_Completing-the-Square-a-≠-1.png)
2.2.9 Use algebra to support and construct proofs (Higher Tier Only)
![edexcel_igcse_mathematics a_topic 13_algebraic manipulation_004_Algebraic Fractions: Numeric (1)](https://resource.studiaacademy.com/wp-content/uploads/2022/05/edexcel_igcse_mathematics-a_topic-13_algebraic-manipulation_004_Algebraic-Fractions_-Numeric-1-3.png)
![edexcel_igcse_mathematics a_topic 13_algebraic manipulation_003_expanding double brackets](https://resource.studiaacademy.com/wp-content/uploads/2022/05/edexcel_igcse_mathematics-a_topic-13_algebraic-manipulation_003_expanding-double-brackets-3.png)