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IB
Math
ematics
SL &
HL
exercise set
1
-
1
-
3
0
v1
Binomial Expansions &
Binomial Theorem
1
© InThinking
–
IB Maths HL & SL
binomial theorem
–
in formula booklet:


1
1
n
nnnrrn
nn
abaababb
r

 
 
  
 
 
 
 
 
 
binomial theorem
–
using sigma notation:


0
n
n
nrr
r
n
abab
r







Exercises
[
answers
on next page ]
Part I
-
questio
ns 1
-
5
▪
no calculator
▪
1.
Perform each of the following expansions.
(a)


4
1
x

(b)


4
1
x

(c
)


4
2
x

2
.
Expand:
(a
)


4
ab

(b
)


4
ab

(c
)


4
3
ab

(d
)


4
32
ab

3
.
Expand
each of the following
:
(a)


5
2
1
x

(b)


5
3
2
xx

(c
)
5
2
4
2
x
x




4
.
Find the term containing
3
x
in the expansion of


4
31
x

.
5
.
Find the
constant term
in the expansion of
6
2
a
a




.
Part I
I
-
questio
ns 6
-
10
▪
calculator
allowed
▪
6
.
Consider
the expansion of


11
2
x

.
(a) Write down the number of terms in this expansion.
(b) Find the term containing
2
x
.
7
.
Find the term
containing
4
x
i
n
the expansion of


7
23
x

.
8
.
The
second term
in the expansion of


4
xp

is
2
150
x
. Find the possible values of
p
.
9
.
Find the coefficient
of
4
x
in the expansion of




24
1
2
1
xx

.
10
.
C
onsider the
expansion
of
6
23
2
2
c
xx
x




. The
constant term is 4
860
. Find the
possible
values
of
c
.
IB
Math
ematics
SL &
HL
exercise set
1
-
1
-
3
0
v1
Binomial Expansions &
Binomial Theorem
2
© InThinking
–
IB Maths HL & SL
ANSWERS
1.
(a)
4
3
2
4
6
4
1
xxxx
   
(b)
432
4
6
4
1
xxxx
   
(c)
4
3
2
8
24
32
16
xxxx
 
 
2.
(a)
4
3
2 2
3
4
4
6
4
aabababb




(b)
4
3
2 2
3
4
4
6
4
aabababb
 


(c
)
4
3
2 2
3
4
81
108
54
12
aabababb




(d
)
4
3
2 2
3
4
81
216
216
96
16
aabababb




3.
(a)
10
8
6
4
2
5
10
10
5
1
xxxxx
    
(b)
15
13
11
9
7
5
10
40
80
80
32
xxxxxx





(c)
82
4
10
16
24
32
16
8
xx
xxx
   
4
.
3
108
x

5.
160
6.
(a) 12 terms (b) 28
160
7.
15 120

8.
5
p

9.
24

10
.
3
c
