Cambridge Additional Mathematics

The “term independent of ”

is the constant term.

x

Counting and the binomial expansion (Chapter 10) 275

EXERCISE 10G

1 Write down the first three and last two terms of the following binomial expansions. Do not simplify

your answers.

a (1 + 2x)^11 b

³

3 x+

2

x

́ 15

c

³

2 x¡

3

x

́ 20

2 Without simplifying, write down:

a the 6 th term of (2x+5)^15 b the 4 th term of

¡

x^2 +y

¢ 9

c the 10 th term of

³

x¡

2

x

́ 17

d the 9 th term of

³

2 x^2 ¡

1

x

́ 21

.

3 In the expansion of (2x+3)^12 , find:

a the coefficient ofx^8 b the coefficient ofx^5.

4 In the expansion of (1¡ 3 x)^10 , find:

a the coefficient ofx^3 b the coefficient ofx^7.

5 In the expansion of

³

x^2 +

2

x

́ 9

, find:

a the coefficient ofx^12 b the constant term c the coefficient ofx¡^6.

6 Consider the expansion of (x+b)^7.

a Write down the general term of the expansion.

b Findbgiven that the coefficient ofx^4 is¡ 280.

7 Find the term independent ofxin the expansion of:

a

³

x+

2

x^2

́ 15

b

³

x¡

3

x^2

́ 9

.

8 Find the coefficient of:

a x^10 in the expansion of (3 + 2x^2 )^10 b x^3 in the expansion of

³

2 x^2 ¡^3

x

́ 6

c x^6 y^3 in the expansion of

¡

2 x^2 ¡ 3 y

¢ 6

d x^12 in the expansion of

³

2 x^2 ¡

1

x

́ 12

.

9 In the expansion of (k+x)^8 , the coefficient ofx^5 is 10 times the coefficient ofx^6. Find the value

ofk.

10 The coefficient ofx^5 in the expansion of (ax¡2)^7 is twice the coefficient ofx^5 in the expansion of

(a+x)^9. Find the value ofa.

11 In the expansion of

³

ax+b

x

́ 6

, the constant term is20 000, and the coefficient ofx^4 is equal to the

coefficient ofx^2.

a Show that ab=10and b=

2 a

5

.

b Findaandbgiven that they are both positive.

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_10\275CamAdd_10.cdr Monday, 23 December 2013 4:41:01 PM BRIAN