Download Factorise

Breaking Brackets
What is Factorisation
Factorise 3a + 3b
Examples
5a + 5
Interactive
2d+8
3e+15
7g-21
10a+5
12b-3
Interactive
4a+6
8d-12
Interactive
Interactive
Interactive
What is Factorisation
Factorisation is the opposite of multiplying.
12 = 6 x 2
6 is a factor of 12
2 is a factor of 12
When you factorise you produce a multiplication sum
12 = 1 x 12
12 = 2 x 6
12 = 3 x 4
The factorisations we normally do in Maths involve letters
3a = 3 x a
5f = 5 x f
7k = 7 x k
ab = a x b
Factorise 3a + 3b
Factorise 3a + 3b
3a + 3b
=3(a+b)
3a
3b
a
b
a+b
a
b
a+b
a
b
a+b
Three rows with ( a + b ) in each row.
The Maths code is 3 ( a + b )
Factorise 7d + 7g
Factorise 7d + 7g
7d + 7g
=7(d+g)
7d
7g
d
g
d+g
d
g
d+g
d
g
d+g
d
g
d+g
d
g
d+g
d
g
d+g
d
g
d+g
Seven rows with ( d + g ) in each row.
The Maths code is 7 ( d + g )
Factorise 8c + 8d
Factorisation is the opposite of multiplying.
In this case a term by a single bracket
x ( ………… )
From the previous examples you probably know that
8c + 8d = 8 ( c + d )
8c +
A method follows
8d
=
8 xc
8 xd
Take
termofand
putnumbers
time signs between
Find each
the HCF
both
numbers and letters
In this case both numbers are the same.
The HCF is 8.
=
Factorisation Opposite of Multiplying a Bracket
8c
x
=
+ 8d
8
(
x
8c = 8 x
8
)
8d = 8 x
Put in brackets and one arrow for each term
Both terms contain 8 so the common factor is
d
8c =8
8cx c
8
Put 8 at the front of the brackets
What do you multiply 8 by to get the two terms
Copy down the sign
c
8c =88dx d
More Examples
Examples
2x + 2y = 2 (
Factorise
x+y )
(a) 7f + 7k
=7(f + k )
9p + 9q = 9 ( p + q
)
(b) 2h + 2j
=2(h + j )
5a + 5e = 5 ( a + e
)
(c) 5t – 5u
=5(t - u )
3s – 3t =
3( s-t
)
(d) 14g – 14k
=14(g - k )
11y – 11t =
11 ( y - t
)
(e) 26b + 26v =26(b + v )
12g – 12w = 12 ( g - w
)
5a + 5b type Examples
a)
3r-3s
3(r-s)
b)
4r-4v
4(r-v)
c)
9r+9w
9(r+w)
d)
7r+7g
7(r+g)
e) 2r-2h
2(r-h)
f)
6s-6v
6(s-v)
g)
8s+8w
8(s+w)
New Examples
Show Answers
0
Ans
(
)
On
(-)
C √ ² h
r
7 8 9 x
s
4
5 6 ÷
v
1
2 3
0
.
- w
= + g
Factorise 5a + 5
+
5a
x
=
5
(
5a = 5 x
5
x
5
)
5=5x
Put in brackets and one arrow for each term
Both terms contain 5 so the common factor is 5
Put 5 at the front of the brackets
What do you multiply 5 by to get the two terms
Copy down the sign
a
1
3a + 3 type Examples
a)
4b+4
4(b+1)
b)
8m+8
8(m+1)
c)
2n-2
2(n-1)
d)
6v+6
6(v+1)
e) 9w+9
9(w+1)
f)
3m+3
3(m+1)
g)
7n+7
7(n+1)
New Examples
Show Answers
0
Ans
(
)
On
(-)
C √ ² w
a
7 8 9 x b
4
5 6 ÷
m
1
2 3
n
0
.
-
= + v
How to Factorise 2d + 8
2d
+
x
x
=
(
8
+
)
Factorising is the opposite
of multiplying the contents
of a bracket
Need to find a number that
you can multiply something to
get 2d and 8.
Find a common factor
by a number ( or a term )
How to Factorise 2d + 8
2d
+
2d is one term
8
8 is the 2nd term
=
2
(
2
d
x
+
)
4
2
x
Concentrate on the
number part of each
… 2 and 8
2d
8
2 x d
2 x 4
2 is a COMMON FACTOR of 2d and 8
In rows
2d + 8
=2(d+4)
2d
8
d
4
d+4
d
4
d+4
Two rows with ( d + 4 ) in each row.
The Maths code is 2 (d + 4 )
How to Factorise 3e + 15
3e
=
3
(
3
e
x
+
15
+
5
Numbers 3 and 15
3 x 5 = 15
3
)
3xe
+
x
3 is a COMMON FACTOR of 3e and 15
3x 5
How to Factorise 7g - 21
7g
=
7
(
7
****
-
e
x
-
21
-
3
Numbers 7 and 21
7 x 3 = 21
7
)
7xg
+
7x 3
x
between 7g and 21
-
in brackets ***********
7 is a COMMON FACTOR of 7g and 21
4a + 12 type Examples
a)
9w-81
b)
7p+28
c)
2q+12
d)
3y-21
0
e) 4z-32
Ans
(
)
On
(-)
f)
6p-30
C √ ² z
g)
8q+16
4
5 6 ÷
p
1
2 3
q
0
.
New Examples
v
7 8 9 x w
Show Answers
-
= + y
How to Factorise 10a + 5
10a
=
5
(
5
5
+
5 x 2 = 10
+
2a
x
Numbers 10 and 5
)
1
5
x
10a
5x2xa
5
+
5 x 2 = 10 …… don’t want 10 want 10a
5 x 2a = 10a
5 is a COMMON FACTOR of 10a and 5
5x 1
How to Factorise 12b - 3
12b
=
3
(
3
4b
3
-
3 x 4 = 12
-
x
Numbers 12 and 3
)
1
3
x
12b
3x4xb
3
-
3 x 4 = 12 …… don’t want 12 want 12b
3 x 4b = 12b
3 is a COMMON FACTOR of 12b and 3
3x 1
12b - 3 type Examples
a)
45d+5
5(9d+1)
b)
12m+4
4(3m+1)
c)
12n-6
6(2n-1)
d)
48e+8
8(6e+1)
e) 12f+3
3(4f+1)
f)
16m+2
2(8m+1)
g)
45n-9
9(5n-1)
New Examples
Show Answers
0
Ans
(
)
On
(-)
C √ ²
f
c
7 8 9 x d
4
5 6 ÷
m
1
2 3
n
0
.
-
= + e
How to Factorise 4a + 6
4a
=
2
(
2
6
+
4x
+
2a
x
Numbers 4 and 6
)
3
2
x
=6
4a
6
2x2xa
+
2x 3
What times table are 4 and 6 both in
2x2=4
2x3=6
2 is a COMMON FACTOR of 4a and 6
How to Factorise 8d - 12
8d
=
4
(
4
12
-
2d
x
Numbers 8 and 12
8x
-
)
3
4
x
= 12
8d
12
4x2xd
-
4x 3
What times table are 8 and 12 both in
2x4=8
2 x 6 = 12
4x2=8
4 x 3 = 12
4 is a COMMON FACTOR of 8d and 12
No Multiple Examples
a)
40s+30
10(4s+3)
b)
12y+9
3(4y+3)
c)
10z-15
5(2z-3)
d)
24g-18
6(4g-3)
e) 25h-20
5(5h-4)
f)
8y-20
4(2y-5)
g)
18z+24
6(3z+4)
Start
New Examples
Show Answers
0
Ans
(
)
On
(-)
C √ ² h
r
7 8 9 x
s
4
5 6 ÷
y
1
2 3
z
0
.
-
= + g