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In order to access this I need to be confident with:
Expanding brackets
Factors and multiples
Factors and multiples
Adding and subtracting Negative numbers
Multiplying Negative Numbers
Multiplying Algebraic Terms
Laws of Indices
Square Numbers
This topic is relevant for:
Here we will learn about factorising expressions into a single bracket.
There are also factorising worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.
Factorising is the reverse process of expanding brackets. To factorise an algebraic expression means to put it in brackets by taking out the common factors.
The reverse process of expanding brackets.
To factorise an algebraic expression means to put it in brackets by taking out the common factors.
3x + 6 = 3(x + 2)
In order to factorise an algebraic expression into a single bracket:
In order to factorise an algebraic expression into a single bracket:
Example 1 – variable in just one term
Fully factorise:
1Find the highest common factor (HCF) of the numbers 3 (the coefficient of
Factors of 3:
1, 3
Factors of 6
1, 6
2, 3
Top tip:
Writing the factor pairs makes it easier to list all the factors
The highest common factor (HCF) of
2Write the highest common factor (HCF) at the front of the single bracket.
3Fill in each term in the bracket by multiplying out.
What do I need to multiply
What do I need to multiply
3(x + 2 )
We can check the answer by multiplying out the bracket!
Example 2 – variable in just one term
Fully factorise:
Find the highest common factor (HCF) of the numbers 14 and 7.
Factors of 14:
1, 14
2, 7
Factors of 7:
1, 7
The highest common factor (HCF) of
Write the highest common factor (HCF) at the front of the single bracket.
Fill in each term in the bracket by multiplying out.
What do I need to multiply
What do I need to multiply
We can check the answer by multiplying out the bracket!
Example 3 – variable in two terms
Fully factorise:
Find the highest common factor (HCF) of the numbers 8 and 12.
Factors of 8:
1, 8
2,4
Factors of 12:
1, 12
2, 6
3, 4
Find the highest common factor (HCF) of the variables
x + x
x
The highest common factor (HCF) of
Write the highest common factor (HCF) at the front of the single bracket.
Fill in each term in the bracket by multiplying out.
What do I need to multiply
What do I need to multiply
We can check the answer by multiplying out the bracket!
Example 4 – variable in two terms
Fully factorise:
Find the highest common factor (HCF) of the numbers 15 and 10.
Factors of 15:
1, 15
3, 5
Factors of 10:
1, 10
2, 5
Find the highest common factor (HCF) of the letters
y
y
The highest common factor (HCF) of
Write the highest common factor (HCF) at the front of the single bracket.
Fill in each term in the bracket by multiplying out.
What do I need to multiply
What do I need to multiply
We can check the answer by multiplying out the bracket!
Example 5 – variable in two out of three terms
Fully factorise:
Find the highest common factor (HCF) of the numbers 6, 2 and 12
Factors of 6:
1, 6
2, 3
Factors of 2:
1, 2
Factors of 12:
1, 12
2, 6
3,4
The highest common factor (HCF) of
Write the highest common factor (HCF) at the front of the single bracket.
Fill in each term in the bracket by multiplying out.
What do I need to multiply
What do I need to multiply
What do I need to multiply
We can check the answer by multiplying out the bracket!
Example 6 – variable in two out of three terms
Fully factorise:
Find the highest common factor (HCF) of the numbers 12, 4 and 8
Factors of 12:
1, 12
2, 6
3,4
Factors of 4:
1, 4
2, 2
Factors of 8:
1, 8
2, 4
Find the highest common factor (HCF) of the letters
x ✕ y
x ✕ y
x ✕ y ✕ y
The highest common factor (HCF) of
Write the highest common factor (HCF) at the front of the single bracket.
Fill in each term in the bracket by multiplying out.
What do I need to multiply
What do I need to multiply
What do I need to multiply
We can check the answer by multiplying out the bracket!
These are some of the common misconceptions around factorising into single brackets
1. Fully factorise: 5x + 10
= 5(x + 2)
2. Fully factorise: 8 – 2y
= 2(4 – y)
3. Fully factorise: 18x2 – 12x
= 6x(3x – 2)
4. Fully factorise: 20y2 + 16xy
= 4y(5y – 4x)
5. Fully factorise: 18 – 6y + 15x
= 3(6 – 2y + 5x)
6. Fully factorise: 12y – 9x2 + 6y2
3y(4 – 3x2 + 2y)
(1)
1. Factorise 5x-20
5(x-4)
(1 mark)
2. Factorise fully: 8x2 + 12xy
4x(2x+3y)
(2 marks)
3. Factorise x2 + 8x
x(x+8)
(1 mark)
Download for free one or more factorising worksheets to help you practise this further and more
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