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Form 3 Mathematics Questions and Answers on Binomial Expansions
Expand and simplify the expression
(
a
+
1
2
)
4
+
(
a
-
1
2
)
4
(5m 28s)
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1.
Expand
(
1
+
1
2
x
)
8
up to the term in
x
3
. By putting x= 0.1, find the approximate value of
(
1.05
)
8
to 2 decimal places.
2.
Write down the first four terms of
(
p
+
q
)
8
using binomial expansion. Use your expansion to evaluate
(
9.99
)
8
to the nearest 100.
3.
Obtain the binomial expansion for
(
1
-
2
x
)
5
. Use your expansion to evaluate
(
0.98
)
5
to five places of decimal.
4.
Use binomial theorem to expand
(
1
-
1
2
x
)
8
up to the fourth term. Use your expansion to evaluate
(
0.98
)
8
by taking x = 0.04
5.
By making use of binomial expansion, determine the value of
(
2.002
)
4
to four decimal places.
6.
Expand
(
1
+
2
x
)
10
up to the term in
x
3
. Hence use your expansion to estimate
(
0.95
)
10
correct to three decimal places.
7.
Expand
(
1
+
a
)
5
. Use your expansion to estimate
(
0.8
)
5
correct to four decimal places.
8.
Expand and simplify
(
1
-
3
x
)
5
, up to the term in
x
3
. Hence use your expansion to estimate
(
0.97
)
5
correct to 4 decimal places.
9.
(a) Write down the simplified expansion of
(
1
+
x
)
6
. (b) Use the expansion up to the fourth term to find the value of
(
1.03
)
6
to the nearest one thousandth.
10.
Expand
(
1
+
x
)
5
, hence, use the expansion to estimate
(
1.04
)
5
correct to 4 decimal places.
11.
Expand
(
2
+
x
)
5
in ascending powers of x up to the term in
x
3
. Hence, approximate the value of
(
2.03
)
5
to 4 s.f.
12.
(a) Expand
(
a
-
b
)
6
(b) Use the first three terms of the expansion in (a) to find the approximate value of
(
1.98
)
6
13.
(a) Expand and simplify the binomial expression
(
2
-
x
)
6
(b) Use the expression up to the term in
x
2
to estimate
(
1.99
)
6
14.
(a) Expand
(
1
+
x
)
5
(b) Use the first three terms of the expansion in (a) to find the approximate value of
(
0.98
)
5
15.
Expand and simplify
(
3
x
-
y
)
4
. Hence use the first three terms of the expansion to approximate the value of
(
60.2
)
4
16.
Use binomial expansion to evaluate
(
2
+
1
√
2
)
5
+
(
2
-
1
√
2
)
5
17.
(a) Expand the expression
(
1
+
1
2
x
)
5
in ascending powers of x, leaving the coefficients as fractions in their simplest form. (b) Use the first three terms of the expansion in (a) above to estimate the value of
(
1
1
20
)
5
18.
(a) Expand and simplify the expression
(
10
+
2
)
5
(b) Use the expansion in (a) above to find the value of
14
5
19.
(a) Expand and simplify the binomial expression
(
2
-
x
)
7
in ascending powers of x. (b) Use the expansion up to the fourth term to evaluate
(
1.97
)
7
correct to 4 decimal places.
20.
(a) Expand and simplify
(
2
-
x
)
5
(b) Use the first 4 terms of the expansion in part (a) above to find the approximate the value of
(
1.8
)
5
to 2 decimal places
21.
Expand and simplify the expression
(
a
+
1
2
)
4
+
(
a
-
1
2
)
4
22.
(a) Expand
(
1
+
x
)
7
up to the
4
t
h
term. (b) Use the expansion in part (a) above to find the approximate value of
(
0.94
)
7
23.
(a) Expand
(
1
-
x
)
5
. (b) Use the expansion in (a) up to the term in
x
3
to approximate the value of
(
0.98
)
5
24.
Expand
(
3
-
x
)
7
up to the term of containing
x
4
. Hence find the approximate value of
(
2.8
)
7
25.
Use the expression of
(
x
-
y
)
5
to evaluate
(
9.8
)
5
correct to 4 decimal places.
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