April 10, 2023

Brackets and factors

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2. Factorising

April 10, 2023

When you factorise, you find numbers and letters that will multiply to make a term.

A group of numbers and letters, such as 4b, 2y or 3x²is known as a term.

Factorising is the opposite of expanding. You end up with an expression involving brackets.

There are a number of simple steps that you need to follow, to factorise an expression.

An expression is made up from two or more terms.

4b + 9 A single number, or letter is still a term.

Explanation

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April 10, 2023

If there are two terms, draw one set of brackets.

8a – 4aFactorising( )

Find the biggest number that will multiply to make the number in both terms. Write it outside the brackets.

4

If there is a letter in each term, write this outside the brackets as well.

a

Work out what you need to multiply the new term you have written outside the bracket, to produce each of the original terms. include the operation symbol, “+”, or “–”.

2 –1

Example

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April 10, 2023

If you have a squared number, treat it as you would a number that isn’t squared.

15x + 9²

3( )

3( )5x

The common highest factor is 3

Divide the first term by 3

Divide the second term by 3, but keep the number squared.

3( )5x +3²

Factorise

Notice that 3 × 3² = 81² = 819 and

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Example

April 10, 2023PractiseFactorise the following…

10x + 5

12x – 8

16x + 8²

9a + 3

16x – 12x

12q² – 18q

5( )2x +1

4( )3x – 2

8( )2x +8

3( )a + 1

4x( )4 – 3

6q ( )2q – 3

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