1. Expanding single brackets
Level 5
a) 5(t+2)
f) 2(8b+2)
k) 6(q+2)
p) 5(2+g) = 5t + = = 6q + =
b) 3(2j+4)
g) 5(9y-3)
l) 8(3e+1)
q) 10(3h+2) = + = = + =
c) 7(k-3)
h) 7(2a-2)
m) 6(r-4)
r) 3(12-z) = - = = - =
d) 6(2w+2)
8(2+k)
n) 5(2u+3)
s) 7(3m+11) = + = = + =
e) 8(p-1)
j) 5(6-2f)
o) 5(4d-2)
t) 4(3-2b) = - = = - =

2. Sheet 3 Sheet 4 a) 5v(t+2) f) 5c(2d+e) a) r(2s+2) f) -2f(t+2) = + = =
Expand the bracket:
Expand the bracket:
a) 5v(t+2)
f) 5c(2d+e)
a) r(2s+2)
f) -2f(t+2) = + = = + =
5tv
2rs
b) -2(y+2)
g) -3(2n-1)
b) -3(2k+3)
g) -3(u-2) = - = = - =
-2y
-6k
c) 5d(e-3)
h) -8k(2-d)
c) 4g(j-2)
h) 3r(-t-2) = - = = - =
d) 7(2t+2)
i) 5v(v+3)
d) -8(m+2)
i) -p(3p+5) = = = =
e) -3(3h+1)
j) 4f(2f-g)
e) 5z(2-t)
j) 6t(7-2t) = = = =

3. Sheet 5 Sheet 6 a) ( + ) f) ( + ) a) ( + ) f) ( + ) 5 t 5 t = 25h + 10
Find the question:
Find the question:
a) ( )
f) ( )
a) ( )
f) ( ) 5 t 5 t
= 25h + 10
= 8k + 12
= 5t + 10
= 5t + 10
b) ( )
g) ( )
b) ( )
g) ( ) 3 3
= 21g + 14
= 9w + 3
= 4u - 6
= 12h + 3
h) ( )
h) ( )
c) ( )
c) ( ) 2 2
= 10f + 8
= 14j- 12
= 2h + 14
= 2j + 4
d) ( )
i) ( )
d) ( )
i) ( )
= 4k + 2
= 6g-3
= 18k - 9
= 9 + 6m
e) ( ) j)
e) ( ) j)
= 18p + 3
= 5c+ 5
= 4m + 6
= 8m - 8

4. Sheet 7 Sheet 8 a) 15h+30 d) 6h+6 a) 30j + 40 d) 15h - 10 b) 12m - 18
When we put expressions into brackets it is called factorising, this is the same as undoing expanding:
When we put expressions into brackets it is called factorising, this is the same as undoing expanding:
Example:
Example:
2(3x-6)
3(2x-4)
6(x-2)
2(3x-6)
3(2x-4)
6(x-2)
Factorise: 6x-12
Factorise: 6x-12
These are all correct answers, but 6(x-2) is the best answer because the number outside the bracket is as big as possible
These are all correct answers, but 6(x-2) is the best answer because the number outside the bracket is as big as possible
(2,3 & 6 are all factors of 6 and 12, but 6 is the h.c.f.)
(2,3 & 6 are all factors of 6 and 12, but 6 is the h.c.f.)
Factorise:
Factorise:
a) 15h+30
d) 6h+6
a) 30j + 40
d) 15h - 10
b) 12m - 18
e) 42k+14
b) 12p + 16
e) g
c) 21b + 7
f) 30n - 20
c) w
f) -6m - 3