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Factorising Expressions
Brackets mean multiply
Extracting common factors means
multiplying the HCF by each term in the
brackets.
2x(3y + 4)
= 6xy + 8x
multiply 2x by each term inside the brackets
2x * 3y = 2 * 3 * x * y = 6 * x * y
= 6xy
Multiplying and dividing squares
a X a = a2
a2 ÷ a = a
2 X 2 = 22
22 ÷ 2 = 2
22 = 4
4÷2=2
Factoring is reverse of
removing brackets
Expanding
Remove brackets
5(2a+3)=10a+15
Factoring
Put in brackets
10a+15=5(2a+3)
Factorising is the reverse of
Extracting
To factorise a number means to
break it up into numbers that can
be multiplied together to get the
original number
The highest common factor HCF is
the largest number that will divide
into both numbers.
Factorise
by
taking out
the HCF.
Example
How to
recognise it
5x + 20
2 terms Find the HCF and put it outside the
How to factorise it
Factors
5(x+4)
brackets
5(
)
Divide both terms by the HCF to find the
factor inside the brackets 5x÷5=x ;
20÷5=4
grouping ac+bc+ad+bd 4 terms Bracket pairs of terms (ac+bc)+ (ad+bd) (c + d)(a + b)
the terms
Take the HCF fm each pair c(a+b)+d(a+b)
Put the common factors in the 1st bracket
quadratic x2 - 8x – 20 3 terms Find the factors of the third term
(x+2)(x-10)
trinomials
a2 + a + n
factors of -20 are …
1 x -20 = -20 ; 2 x -10 = -20 ; 4 x -5 = -20
5 x -4 = -20 ; 10 x -2 = -20 ; 20 x -1 = -20
Pick the factors which form the middle
term when added 2+ -10 = -8
using the 25a2 – 16b2 square Find the square root of both terms
(5a+4b)(5a-4b)
Difference
- square (5)2 = 25 : (a)2 = a2 : (4)2 = 16 : (b)2 = b2
of 2
Use the rule a2– b2 = (a–b)(a+b)
squares
Types of factorising
Factorise by
Example
Factors
taking out the HCF.
5x + 20
5(x+4)
grouping the terms
ac + bc + ad + bd
(c + d)(a + b)
quadratic trinomials
x2 - 8x – 20
(x+2)(x-10)
using the difference of
2 squares
using the difference of
2 squares and
hence evaluate
25a2 – 16b2
(5a+4b)(5a-4b)
62 - 52
(6+5)(6-5)
= (11)(1)
= 11 multiplied by 1
= 11