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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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