🔢 Mastering Algebraic Manipulation Made Easy!

Algebra is a universal language of patterns and relationships. Being able to **simplify, expand, and factorise** expressions quickly is essential for acing O-Level exams—these skills cut through messy questions and reveal the answers faster.

Main Concept: Simplify, Expand, Factorise

We usually start by simplifying terms (collecting like terms), then **expanding** products such as

(a+b)(c+d)

, and finally **factorising**—the reverse process—by taking out common factors or reversing double brackets. Mastery of these moves turns long algebra questions into one-liners!

Combine like terms: $3x + 7x = 10x$
Expand brackets: $(2x-5)(x+4) = 2x^2 + 3x - 20$
Factorise common factor: $6xy - 9y = 3y(2x - 3)$
Factorise quadratic form: $x^2 + 2x - 35 = (x+7)(x-5)$

Worked Example: Expand & Factorise in One Go

Problem: Simplify

\;(2x + 3)(x - 4) + 5x\,

and then factorise the final answer.

Step 1: Expand $(2x + 3)(x - 4) \;\Rightarrow\; 2x \times x + 2x \times (-4) + 3 \times x + 3 \times (-4) = 2x^2 - 8x + 3x - 12$
Step 2: Combine like terms: $2x^2 - 5x - 12$
Step 3: Add $5x$ : $2x^2 - 5x - 12 + 5x = 2x^2 - 12$
Step 4: Factorise common factor $2$ : $2x^2 - 12 = 2(x^2 - 6)$

Practice makes perfect! Work through past-paper questions, time yourself, and always check by expanding your factorised answers. The more you wrestle with algebra, the faster and more accurate you’ll become.