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Expanding brackets Expand and simplify Factors and multiples Powers and roots Algebraic expressions Adding and subtracting negative numbers Multiplying and dividing negative numbers Highest common factor Laws of indices Square numbers and square rootsThis topic is relevant for:
Here we will learn about factorising to single brackets by finding the highest common factor.
There are also factorising to single brackets worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if youβre still stuck.
In order to factorise an algebraic expression into a single bracket:
We can factorise lots of different types of expressions into single brackets including some quadratics like
For quadratic expressions of the form
Check out our main factorising lesson for a complete summary of all the different ways we can factorise expressions, and then explore our other factorising lessons for detailed step-by-step guides and worksheets on each type.
Get your free factorising single brackets worksheet of 20+ questions and answers. Includes reasoning and applied questions.
DOWNLOAD FREEGet your free factorising single brackets worksheet of 20+ questions and answers. Includes reasoning and applied questions.
DOWNLOAD FREEFully factorise:
1Find the highest common factor (HCF) of the numbers
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
We can check the answer by multiplying out the bracket!
Fully factorise:
Find the highest common factor (HCF) of the numbers 14 and 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
(don’t forget to keep the – here)
We can check the answer by multiplying out the bracket!
Fully factorise:
Find the highest common factor (HCF) of the numbers 8 and 12.
Find the highest common factor (HCF) of the variables
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!
Fully factorise:
Find the highest common factor (HCF) of the numbers 15 and 10.
Find the highest common factor (HCF) of the letters
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!
Fully factorise:
Find the highest common factor (HCF) of the numbers 6, 2 and 12
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
Donβt forget to keep the – here!
We can check the answer by multiplying out the bracket!
Fully factorise:
Find the highest common factor (HCF) of the numbers 12, 4 and 8
Find the highest common factor (HCF) of the letters
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
Donβt forget to keep the – here!
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+10)
5x(x+2)
5(x+2)
x(5+10)
The highest common factor of 5 and 10 is 5 . We can divide each term in the original expression by 5 , which means the bracket must contain (x+2) .
2. Fully factorise: 8-2y
The highest common factor of 8 and 2 is 2 . We can divide each term in the original expression by 2 ; the bracket must contain a minus sign just like the original expression.
3. Fully factorise: 18x^{2}-12x
3x(6x-4)
6(3x^{2}-2x)
3(6x^{2}-4x)
6x(3x-2)
The highest common factor of 18x^{2} and 12x is 6x . We can divide each term by 6x , which means the bracket must contain (3x-2) .
4. Fully factorise: 20y^{2}+16xy
4y(5y-4x)
y(20y-16x)
2y(10y-8x)
4xy(5y-4x)
The highest common factor of 20y^{2} and 16xy is 4y . We can divide each term by 4y , which means the bracket must contain (5y-4x) .
5. Fully factorise: 18-6y+15x
3xy(6-2y+5x)
3(6-2y+5x)
18(1-2y+5x)
3(6+2y+5x)
The highest common factor of 18,6y and 15x is 3 . We can divide each term by 3 , which means the bracket must contain (6-2y+5x) .
6. Fully factorise: 12y-9x^{2}y+6y^{2}
12y(1-3x^{2}+2y)
3y(4+3x^{2}+2y)
3y(4-3x^{2}+2y)
3y(4-3x^{2}-2y)
The highest common factor of 12y, 9x^{2}y and 6y^{2} is 3y . We can divide each term by 3y , which means the bracket must contain (4-3x^{2}+2y) .
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