Factorising into Single Brackets

When we factorise an expression, we’re doing the opposite of expanding. Instead of multiplying out brackets, we’re putting an expression into brackets. Think of it like grouping similar items together

 

What is Factorising?

Factorising is like finding what’s common between terms and grouping it outside a bracket. This involves identifying a common factor that each term shares and then writing it outside the bracket.

 

Key Steps for Factorising Single Brackets

1. Identify the Common Factor: Look at each term in the expression and find the largest factor (number or variable) that’s common.
2. Factor it Out: Write this common factor outside a bracket.
3. Fill the Bracket: Inside the bracket, write what you’d need to multiply by the common factor to get each term.

 

Example 1 : Factorising an Algebraic Expression

Factorise: $6x + 9$.

Step-by-Step Solution:

1. Identify the common factor: The numbers 6 and 9 share a common factor of 3.
2. Factor it out: Write 3 outside a bracket: $$6x + 9 = 3( ? + ? )$$
3. Fill the bracket: $$6x \div 3 = 2x \\ 9 \div 3 = 3 \\ \text{So,} \\ 6x + 9 = 3(2x + 3)$$

 

 

 

 

Example 2 : Factorising an Algebraic Expression

Factorise: $12x^2 + 18x$

Step-by-Step Solution:

1. Identify the common factor: Both terms have 6 as a common factor for the numbers and $x$ as a common variable
2. Factor it out: Write $6x$ outside the bracket: $$12x^2 + 18x = 6x( ? + ? )$$
3. Fill the bracket:$$12x^2 \div 6x = 2x \\ 18x \div 6x = 3 \\ \text{So,} \\ 12x^2 + 18x = 6x(2x + 3)$$